Natasha Samko - Academia.edu (original) (raw)

Papers by Natasha Samko

Research paper thumbnail of On Hardy-Type Inequalities as an Intellectual Adventure for 100 Years

Journal of mathematical sciences, Feb 2, 2024

Research paper thumbnail of Errata: On Non-Equilibrated Almost Monotonic Functions of the Zygmund-Bary-Stechkin Class

Real analysis exchange, 2007

Research paper thumbnail of Criterion for the Fredholmness of Singular Operators with Piecewise Continuous Coefficients in Generalized Hölder Spaces with Weight

Birkhäuser Basel eBooks, 2003

In a previous paper we found conditions for a singular integral operator with piecewise continuou... more In a previous paper we found conditions for a singular integral operator with piecewise continuous coefficients to be Fredholm in a weighted generalized Holder space H 0 ω (Γ, ρ) together with a formula for the index. The conditions were given in terms of Boyd-type indices of the space H 0 ω (Γ, ρ). In this paper we prove that those conditions are also necessary for a singular integral operator to be Fredholm.

Research paper thumbnail of Weighted Inequalities of Hardy Type

WORLD SCIENTIFIC eBooks, Apr 12, 2017

Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Opera... more Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Operator Higher Order Hardy Inequalities Fractional Order Hardy Inequalities Integral Operators on the Cone of Monotone Functions.

Research paper thumbnail of Some New Scales of Weight Characterizations of Hardy-type Inequalities

In this paper we present, discuss and illustrate some new scales of conditions to characterize mo... more In this paper we present, discuss and illustrate some new scales of conditions to characterize modern forms of Hardy′s inequalities which can not be found in the newest books in this area. Moreover, some results of importance as motivation for these scales are presented and discussed in a historical perspective.

Research paper thumbnail of New and Complementary Results

Research paper thumbnail of On a Muckenhoupt-type condition for Morrey spaces

arXiv (Cornell University), Sep 29, 2011

Research paper thumbnail of Oscillating Zygmund-Bary-Stechkin characteristics and Fredholmness of singular integral operators in the Holder spaces with oscillating characteristics and oscillating weights

We consider quasi-monotonic functions of the Zygmund-Bary-Stechkin class Z with the main emphasis... more We consider quasi-monotonic functions of the Zygmund-Bary-Stechkin class Z with the main emphasis on properties of the index numbers of functions in this class (of Boyd type indices). A special attention is paid to functions whose lower and upper index numbers do not coincide with each other (non-equilibrated functions). It is proved that the bounds for functions in Z known in terms of these indices, are exact in a certain sense. We also single out some special family of non-equilibrated functions in Z which oscillate in a certain way between two power functions. Given two numbers 0 < a < b < 1, we explicitly construct examples of functions in Z for which a and b serve as the index numbers. Moreover, for a certain class of function oscillating between two power functions there is given an explicit formula for calculation of the indices. The developed properties of functions in this class are applied to an investigation of the normal solvability of some singular integral operators in weighted spaces with prescribed oscillating modulus of continuity and oscillating weights.

Research paper thumbnail of Some remarks and new developments concerning Hardy-type inequalities

Research paper thumbnail of Weighted Hardy and singular operators in Morrey spaces

arXiv (Cornell University), Aug 18, 2008

We study the weighted boundedness of the Cauchy singular integral operator S Γ in Morrey spaces L... more We study the weighted boundedness of the Cauchy singular integral operator S Γ in Morrey spaces L p,λ (Γ) on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L p,λ (0, ℓ), ℓ > 0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.

Research paper thumbnail of Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces

Mathematische Nachrichten, Apr 3, 2018

Research paper thumbnail of On some hyperbolic type equations and weighted anisotropic Hardy operators

Mathematical Methods in The Applied Sciences, Jul 1, 2016

Research paper thumbnail of Sharpness of some Hardy-type inequalities

arXiv (Cornell University), Feb 18, 2023

Research paper thumbnail of Singular operators in variable spaces Lp (·)(,P) with oscillating weights

Mathematische Nachrichten, 2007

Research paper thumbnail of On compactness of integral operators with a generalized weak singularity in weighted spaces of continuous functions with a given continuity modulus

Research paper thumbnail of Zygmund-type estimates for fractional integration and differentiation operators of variable order

Russian Mathematics, 2011

ABSTRACT We consider non-standard generalized Hölder spaces of functions defined on a segment of ... more ABSTRACT We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant. Keywords and phrasesfractional integration operators–fractional differentiation operators–generalized continuity modulus–generalized Hölder spaces

Research paper thumbnail of Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications

Analysis and mathematical physics, May 30, 2024

Research paper thumbnail of A note on contributions concerning nonseparable spaces with respect to signal processing within Bayesian frameworks

Mathematical Methods in the Applied Sciences

In this paper, we discuss the study of some signal processing problems within Bayesian frameworks... more In this paper, we discuss the study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable. For applications, the suggested approach may be of interest in situations where approximation in the norm of the space is not possible. We describe the idea for the case of the abstract Cauchy problem for the evolution equation and provide more detailed example of the diffusion equation with the initial data in the nonseparable Morrey space.

Research paper thumbnail of On some results in weighted Morrey spaces with applications to PDE

Research paper thumbnail of Preface: Special issue on harmonic analysis, applied mathematics and engineering problems

Nonlinear Studies, 2019

This special issue "Harmonic Analysis, Applied Mathematics and Engineering Problems", d... more This special issue "Harmonic Analysis, Applied Mathematics and Engineering Problems", dedicated to 75th anniversary of Professor Lars-Erik Persson, contains papers on various topics in pure and applied mathematics including, in particular, such areas as harmonic analysis, function spaces, inequalities, homogenization theory, differential equations and some applied and engineering problems. It is well known that modern research in applied sciences is profoundly intertwined with such areas of pure mathematics as functional analysis, operator theory, and harmonic analysis. Thus, the methods and results of these areas are fundamental tools in the study of a variety of problems in applied sciences. The increasing complexity of the mathematical models in applications requires more advanced mathematical tools. This encourages researchers to look for new dependencies and/or descriptions in the mathematical models of the phenomena under the study that could lead to a refinement of ...

Research paper thumbnail of On Hardy-Type Inequalities as an Intellectual Adventure for 100 Years

Journal of mathematical sciences, Feb 2, 2024

Research paper thumbnail of Errata: On Non-Equilibrated Almost Monotonic Functions of the Zygmund-Bary-Stechkin Class

Real analysis exchange, 2007

Research paper thumbnail of Criterion for the Fredholmness of Singular Operators with Piecewise Continuous Coefficients in Generalized Hölder Spaces with Weight

Birkhäuser Basel eBooks, 2003

In a previous paper we found conditions for a singular integral operator with piecewise continuou... more In a previous paper we found conditions for a singular integral operator with piecewise continuous coefficients to be Fredholm in a weighted generalized Holder space H 0 ω (Γ, ρ) together with a formula for the index. The conditions were given in terms of Boyd-type indices of the space H 0 ω (Γ, ρ). In this paper we prove that those conditions are also necessary for a singular integral operator to be Fredholm.

Research paper thumbnail of Weighted Inequalities of Hardy Type

WORLD SCIENTIFIC eBooks, Apr 12, 2017

Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Opera... more Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Operator Higher Order Hardy Inequalities Fractional Order Hardy Inequalities Integral Operators on the Cone of Monotone Functions.

Research paper thumbnail of Some New Scales of Weight Characterizations of Hardy-type Inequalities

In this paper we present, discuss and illustrate some new scales of conditions to characterize mo... more In this paper we present, discuss and illustrate some new scales of conditions to characterize modern forms of Hardy′s inequalities which can not be found in the newest books in this area. Moreover, some results of importance as motivation for these scales are presented and discussed in a historical perspective.

Research paper thumbnail of New and Complementary Results

Research paper thumbnail of On a Muckenhoupt-type condition for Morrey spaces

arXiv (Cornell University), Sep 29, 2011

Research paper thumbnail of Oscillating Zygmund-Bary-Stechkin characteristics and Fredholmness of singular integral operators in the Holder spaces with oscillating characteristics and oscillating weights

We consider quasi-monotonic functions of the Zygmund-Bary-Stechkin class Z with the main emphasis... more We consider quasi-monotonic functions of the Zygmund-Bary-Stechkin class Z with the main emphasis on properties of the index numbers of functions in this class (of Boyd type indices). A special attention is paid to functions whose lower and upper index numbers do not coincide with each other (non-equilibrated functions). It is proved that the bounds for functions in Z known in terms of these indices, are exact in a certain sense. We also single out some special family of non-equilibrated functions in Z which oscillate in a certain way between two power functions. Given two numbers 0 < a < b < 1, we explicitly construct examples of functions in Z for which a and b serve as the index numbers. Moreover, for a certain class of function oscillating between two power functions there is given an explicit formula for calculation of the indices. The developed properties of functions in this class are applied to an investigation of the normal solvability of some singular integral operators in weighted spaces with prescribed oscillating modulus of continuity and oscillating weights.

Research paper thumbnail of Some remarks and new developments concerning Hardy-type inequalities

Research paper thumbnail of Weighted Hardy and singular operators in Morrey spaces

arXiv (Cornell University), Aug 18, 2008

We study the weighted boundedness of the Cauchy singular integral operator S Γ in Morrey spaces L... more We study the weighted boundedness of the Cauchy singular integral operator S Γ in Morrey spaces L p,λ (Γ) on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L p,λ (0, ℓ), ℓ > 0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.

Research paper thumbnail of Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces

Mathematische Nachrichten, Apr 3, 2018

Research paper thumbnail of On some hyperbolic type equations and weighted anisotropic Hardy operators

Mathematical Methods in The Applied Sciences, Jul 1, 2016

Research paper thumbnail of Sharpness of some Hardy-type inequalities

arXiv (Cornell University), Feb 18, 2023

Research paper thumbnail of Singular operators in variable spaces Lp (·)(,P) with oscillating weights

Mathematische Nachrichten, 2007

Research paper thumbnail of On compactness of integral operators with a generalized weak singularity in weighted spaces of continuous functions with a given continuity modulus

Research paper thumbnail of Zygmund-type estimates for fractional integration and differentiation operators of variable order

Russian Mathematics, 2011

ABSTRACT We consider non-standard generalized Hölder spaces of functions defined on a segment of ... more ABSTRACT We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant. Keywords and phrasesfractional integration operators–fractional differentiation operators–generalized continuity modulus–generalized Hölder spaces

Research paper thumbnail of Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications

Analysis and mathematical physics, May 30, 2024

Research paper thumbnail of A note on contributions concerning nonseparable spaces with respect to signal processing within Bayesian frameworks

Mathematical Methods in the Applied Sciences

In this paper, we discuss the study of some signal processing problems within Bayesian frameworks... more In this paper, we discuss the study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable. For applications, the suggested approach may be of interest in situations where approximation in the norm of the space is not possible. We describe the idea for the case of the abstract Cauchy problem for the evolution equation and provide more detailed example of the diffusion equation with the initial data in the nonseparable Morrey space.

Research paper thumbnail of On some results in weighted Morrey spaces with applications to PDE

Research paper thumbnail of Preface: Special issue on harmonic analysis, applied mathematics and engineering problems

Nonlinear Studies, 2019

This special issue "Harmonic Analysis, Applied Mathematics and Engineering Problems", d... more This special issue "Harmonic Analysis, Applied Mathematics and Engineering Problems", dedicated to 75th anniversary of Professor Lars-Erik Persson, contains papers on various topics in pure and applied mathematics including, in particular, such areas as harmonic analysis, function spaces, inequalities, homogenization theory, differential equations and some applied and engineering problems. It is well known that modern research in applied sciences is profoundly intertwined with such areas of pure mathematics as functional analysis, operator theory, and harmonic analysis. Thus, the methods and results of these areas are fundamental tools in the study of a variety of problems in applied sciences. The increasing complexity of the mathematical models in applications requires more advanced mathematical tools. This encourages researchers to look for new dependencies and/or descriptions in the mathematical models of the phenomena under the study that could lead to a refinement of ...