Fractional Hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva; Juha Lehrbäck; Heli Tuominen; Antti V. Vähäkangas

Displaying similar documents to “Fractional Hardy inequalities and visibility of the boundary”

A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization

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Hardy inequality of fractional order.

Gurka, Petr, Opic, Bohumír (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Fractional Hardy inequality with a remainder term

Bartłomiej Dyda (2011)

Colloquium Mathematicae

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We prove a Hardy inequality for the fractional Laplacian on the interval with the optimal constant and additional lower order term. As a consequence, we also obtain a fractional Hardy inequality with the best constant and an extra lower order term for general domains, following the method of M. Loss and C. Sloane [J. Funct. Anal. 259 (2010)].

Fractional Hardy-Sobolev-Maz'ya inequality for domains

Bartłomiej Dyda, Rupert L. Frank (2012)

Studia Mathematica

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We prove a fractional version of the Hardy-Sobolev-Maz’ya inequality for arbitrary domains and $L^{p}$ norms with p ≥ 2. This inequality combines the fractional Sobolev and the fractional Hardy inequality into a single inequality, while keeping the sharp constant in the Hardy inequality.

Vector-valued inequalities for the commutators of fractional integrals with rough kernels

Yanping Chen, Xinfeng Wu, Honghai Liu (2014)

Studia Mathematica

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Some conditions implying vector-valued inequalities for the commutator of a fractional integral and a fractional maximal operator are established. The results obtained are substantial improvements and extensions of some known results.

Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents

Hongbin Wang, Chenchen Niu (2024)

Czechoslovak Mathematical Journal

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We introduce a type of $n$ -dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.

Quelques inégalités concernant l'aréa-fonction

M. Jevtić (1982)

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Weighted norm inequalities for multilinear fractional operators on Morrey spaces

Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka (2011)

Studia Mathematica

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A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.

Existence of solutions of generalized fractional differential equation with nonlocal initial condition

Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)

Mathematica Bohemica

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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.