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Papers by A. Karapetyants

Research paper thumbnail of A Practical Method for Solving the Inverse Quantum Scattering Problem on a Half Line

Journal of Physics: Conference Series

Research paper thumbnail of Mixed norm Bergman–Morrey-type spaces on the unit disc

We introduce and study the mixed-norm Bergman-Morrey space A q;p,λ (D), mixednorm Bergman-Morrey ... more We introduce and study the mixed-norm Bergman-Morrey space A q;p,λ (D), mixednorm Bergman-Morrey space of local type A q;p,λ loc (D), and mixed-norm Bergman-Morrey space of complementary type A q;p,λ (D) on the unit disk D in the complex plane C. The mixed norm Lebesgue-Morrey space L q;p,λ (D) is defined by the requirement that the sequence of Morrey L p,λ (I)-norms of the Fourier coefficients of a function f belongs to l q (I = (0, 1)). Then, A q;p,λ (D) is defined as the subspace of analytic functions in L q;p,λ (D). Two other spaces A q;p,λ loc (D) and A q;p,λ (D) are defined similarly by using the local Morrey L p,λ loc (I)-norm and the complementary Morrey L p,λ (I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces.

Research paper thumbnail of On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces

Research paper thumbnail of On Grand and Small Bergman Spaces

Research paper thumbnail of Dynamics of Properties of Toeplitz Operators with Radial Symbols

Research paper thumbnail of On Boundedness of Bergman Projection Operators in Banach Spaces of Holomorphic Functions in Half-Plane and Harmonic Functions in Half-Space

Journal of Mathematical Sciences

Research paper thumbnail of Dynamics of Properties of Toeplitz Operators with Radial Symbols

Integral Equations and Operator Theory, 2004

Research paper thumbnail of Estimates for twisted convolution operators with singularities of kernels on a sphere and at the origin

Differential Equations, 2006

Research paper thumbnail of Spaces BMOp(.)(D) of a variable exponent p(z)

We introduce and describe the spaces BMO p(·) (D), 1 ≤ p(z) < ∞ of functions of bounded mean osci... more We introduce and describe the spaces BMO p(·) (D), 1 ≤ p(z) < ∞ of functions of bounded mean oscillation over unit disc in the complex plane in the hyperbolic Bergman metric with respect to the Lebesgue measure and variable exponent p = p(z).

Research paper thumbnail of On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols

Integral Equations and Operator Theory, 2001

We describe the Fredholm symbol algebra for the C*-al~ebra generated by two dimensional singular ... more We describe the Fredholm symbol algebra for the C*-al~ebra generated by two dimensional singular integral operators, acting on L2(]R ), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin. These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.

Research paper thumbnail of A Practical Method for Solving the Inverse Quantum Scattering Problem on a Half Line

Journal of Physics: Conference Series

Research paper thumbnail of Mixed norm Bergman–Morrey-type spaces on the unit disc

We introduce and study the mixed-norm Bergman-Morrey space A q;p,λ (D), mixednorm Bergman-Morrey ... more We introduce and study the mixed-norm Bergman-Morrey space A q;p,λ (D), mixednorm Bergman-Morrey space of local type A q;p,λ loc (D), and mixed-norm Bergman-Morrey space of complementary type A q;p,λ (D) on the unit disk D in the complex plane C. The mixed norm Lebesgue-Morrey space L q;p,λ (D) is defined by the requirement that the sequence of Morrey L p,λ (I)-norms of the Fourier coefficients of a function f belongs to l q (I = (0, 1)). Then, A q;p,λ (D) is defined as the subspace of analytic functions in L q;p,λ (D). Two other spaces A q;p,λ loc (D) and A q;p,λ (D) are defined similarly by using the local Morrey L p,λ loc (I)-norm and the complementary Morrey L p,λ (I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces.

Research paper thumbnail of On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces

Research paper thumbnail of On Grand and Small Bergman Spaces

Research paper thumbnail of Dynamics of Properties of Toeplitz Operators with Radial Symbols

Research paper thumbnail of On Boundedness of Bergman Projection Operators in Banach Spaces of Holomorphic Functions in Half-Plane and Harmonic Functions in Half-Space

Journal of Mathematical Sciences

Research paper thumbnail of Dynamics of Properties of Toeplitz Operators with Radial Symbols

Integral Equations and Operator Theory, 2004

Research paper thumbnail of Estimates for twisted convolution operators with singularities of kernels on a sphere and at the origin

Differential Equations, 2006

Research paper thumbnail of Spaces BMOp(.)(D) of a variable exponent p(z)

We introduce and describe the spaces BMO p(·) (D), 1 ≤ p(z) < ∞ of functions of bounded mean osci... more We introduce and describe the spaces BMO p(·) (D), 1 ≤ p(z) < ∞ of functions of bounded mean oscillation over unit disc in the complex plane in the hyperbolic Bergman metric with respect to the Lebesgue measure and variable exponent p = p(z).

Research paper thumbnail of On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols

Integral Equations and Operator Theory, 2001

We describe the Fredholm symbol algebra for the C*-al~ebra generated by two dimensional singular ... more We describe the Fredholm symbol algebra for the C*-al~ebra generated by two dimensional singular integral operators, acting on L2(]R ), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin. These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.