On Generalized Spherical Fractional Integration Operators in Weighted Generalized Hölder Spaces on the Unit Sphere
For spherical convolution operators with a given power type asymptotic of their Fourier-Laplace multiplier we prove a statement on the boundedness within the framework of weighted generalized Hölder spaces on the unit sphere. The result obtained explicitly shows how spherical convolution operators under consideration improve the behavior of the continuity modulus of functions.
Keywordsspherical convolution operators spherical potentials indices of almost monotonic functions Boyd-type indices continuity modulus generalized Hölder spaces
Unable to display preview. Download preview PDF.
- N.G. Samko. On boundedness of singular operator in weighted generalized Hölder spaces H 0ω (Г, ρ) in terms of upper and lower indices of these spaces (in Russian). Deponierted in VINITI, no. 349-B91, 28p., Moscow, 1991.Google Scholar
- B.G. Vakulov. Spherical convolution operators in the case of power decreasing of its multiplier (Russian). Deponierted in VINITI, no. 6545-83, Moscow, 1983.Google Scholar
- B.G. Vakulov. Hardy-Littlewood-Sobolev theorems on potential type operators in L p(S n−1, ρ). Deponierted in VINITI, no. 5435-86, 41p., Moscow, 1986.Google Scholar
- B.G. Vakulov. Potential type operators on a sphere in generalized Hölder spaces. Deponierted in VINITI, no. 1563-86, 31p., Moscow, 1986.Google Scholar
- B.G. Vakulov, N.K. Karapetiants, and L.D. Shankishvili. Spherical convolution operators with a power-logarithmic kernel in generalized Hölder spaces. Izv. Vyssh. Uchebn. Zaved. Mat., (2): 3–14, 2003.Google Scholar