Displaying similar documents to “On maximal functions of fractional order”

Fractional Hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas (2014)

Studia Mathematica

Similarity:

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.

Fractional Hardy inequality with a remainder term

Bartłomiej Dyda (2011)

Colloquium Mathematicae

Similarity:

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

Similarity:

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.

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

Hongbin Wang, Chenchen Niu (2024)

Czechoslovak Mathematical Journal

Similarity:

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.