Displaying similar documents to “Radial derivative on bounded symmetric domains”

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.

Hardy and Rellich type inequalities with remainders

Ramil Nasibullin (2022)

Czechoslovak Mathematical Journal

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Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011)...

On Hardy spaces on worm domains

Alessandro Monguzzi (2016)

Concrete Operators

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In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting...