The inversion of fractional integrals on a sphere

DOI10.1007/BF02764802zbMath0778.46025MaRDI QIDQ1802752

Boris Rubin

Publication date: 29 June 1993

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

inverse operatorspherical harmonicspotential operatorfractional integralfractional smoothnesssurface elementNoetherian operator\(d\)-characteristicLiouville type spaceMarchaud difference regularization of one- dimensional divergent integralsmean values over planar sectionsRiesz type potentialspherical hypersingular operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) (Semi-) Fredholm operators; index theories (47A53)

Related Items

Weighted inequalities for the Riesz potential on the sphere ⋮ A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

Cites Work

• Generalized Riesz potentials and hypersingular integrals with homogeneous characteristics, their symbols and inversion
• Lipschitz spaces on the surface of the unit sphere in Euclidean n-space
• Lipschitz spaces of distributions on the surface of unit sphere in Euclidean n-space
• On the behavior of special classes of ultraspherical expansions. I, II
• Spherical Fractional Integrals
• Classical Expansions and Their Relation to Conjugate Harmonic Functions
• Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
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