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Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets

100%
Dyda B.
Studia Mathematica
|
2010
|
tom 197
|
nr 3
247-256
EN
We prove norm inequalities between Lorentz and Besov-Lipschitz spaces of fractional smoothness.
2
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Fractional Hardy inequality with a remainder term

100%
Dyda B.
Colloquium Mathematicum
|
2011
|
tom 122
|
nr 1
59-67
EN
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)].
3
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Fractional Hardy-Sobolev-Maz'ya inequality for domains

63%
Dyda B., Frank R.
Studia Mathematica
|
2012
|
tom 208
|
nr 2
151-166
EN
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.
4
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Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains

63%
Bogdan K., Dyda B.
Studia Mathematica
|
2003
|
tom 157
|
nr 1
83-96
EN
For $C^{1,1}$ domains we give exact asymptotics near the domain's boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.
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