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Generalized Hölder type spaces of harmonic functions in the unit ball and half space

Alexey KarapetyantsJoel Esteban Restrepo — 2020

Czechoslovak Mathematical Journal

We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity ω = ω ( h ) and the second is the variable exponent harmonic Hölder space with the continuity modulus | h | λ ( · ) . We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Karapetyants, AlexeyKarasev, DenisNogin, Vladimir — 2005

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15. We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given. * This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.

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