Mukta Bhandari | Chowan University (original) (raw)
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Papers by Mukta Bhandari
We establish a good lambda inequality relating to the distribution function of Riesz potential an... more We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on (R, dμ) where μ is a positive Radon measure which doesn’t necessarily satisfy a doubling condition. This is extended to weights w in A∞(μ) associated to the measure μ. We also derive potential inequalities as an application.
The main focus of this work is to study the classical Calderón-Zygmund theory and its recent deve... more The main focus of this work is to study the classical Calderón-Zygmund theory and its recent developments. An attempt has been made to study some of its theory in more generality in the context of a nonhomogeneous space equipped with a measure which is not necessarily doubling. We establish a Hedberg type inequality associated to a non-doubling measure which connects two famous theorems of Harmonic Analysis-the Hardy-Littlewood-Weiner maximal theorem and the Hardy-Sobolev integral theorem. Hedberg inequalities give pointwise estimates of the Riesz potentials in terms of an appropriate maximal function. We also establish a good lambda inequality relating the distribution function of the Riesz potential and the fractional maximal function in (R, dμ), where μ is a positive Radon measure which is not necessarily doubling. Finally, we also derive potential inequalities as an application. INEQUALITIES ASSOCIATED TO RIESZ POTENTIALS AND NON-DOUBLING MEASURES WITH APPLICATIONS by MUKTA BAHA...
We know that a continuous function on a closed interval satisfies the Intermediate Value Property... more We know that a continuous function on a closed interval satisfies the Intermediate Value Property. Likewise, the derivative function of a differentiable function on a closed interval satisfies the IVP property which is known as the Darboux theorem in any real analysis course. Most of the proofs found in the literature use the Extreme Value Property of a continuous function. In this paper, I am going to present a simple and elegant proof of the Darboux theorem using the Intermediate Value Theorem and the Rolles theorem
We establish a good lambda inequality relating to the distribution function of Riesz potential an... more We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on (R, dμ) where μ is a positive Radon measure which doesn’t necessarily satisfy a doubling condition. This is extended to weights w in A∞(μ) associated to the measure μ. We also derive potential inequalities as an application.
The main focus of this work is to study the classical Calderón-Zygmund theory and its recent deve... more The main focus of this work is to study the classical Calderón-Zygmund theory and its recent developments. An attempt has been made to study some of its theory in more generality in the context of a nonhomogeneous space equipped with a measure which is not necessarily doubling. We establish a Hedberg type inequality associated to a non-doubling measure which connects two famous theorems of Harmonic Analysis-the Hardy-Littlewood-Weiner maximal theorem and the Hardy-Sobolev integral theorem. Hedberg inequalities give pointwise estimates of the Riesz potentials in terms of an appropriate maximal function. We also establish a good lambda inequality relating the distribution function of the Riesz potential and the fractional maximal function in (R, dμ), where μ is a positive Radon measure which is not necessarily doubling. Finally, we also derive potential inequalities as an application. INEQUALITIES ASSOCIATED TO RIESZ POTENTIALS AND NON-DOUBLING MEASURES WITH APPLICATIONS by MUKTA BAHA...
We know that a continuous function on a closed interval satisfies the Intermediate Value Property... more We know that a continuous function on a closed interval satisfies the Intermediate Value Property. Likewise, the derivative function of a differentiable function on a closed interval satisfies the IVP property which is known as the Darboux theorem in any real analysis course. Most of the proofs found in the literature use the Extreme Value Property of a continuous function. In this paper, I am going to present a simple and elegant proof of the Darboux theorem using the Intermediate Value Theorem and the Rolles theorem