Pointwise Estimates for Block-Radial Functions of Sobolev Classes

The paper gives sharp pointwise estimates for functions belonging to H ˙ s , p ( R N ) with radial symmetry in m blocks of variables, for m < s p < N . The estimates are formulated in terms of multiradial monomials. The form of the monomials depends on the structure of the group of block-radia...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2019-04, Vol.25 (2), p.321-344
Main Authors: Skrzypczak, Leszek, Tintarev, Cyril
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Estimates
Fourier Analysis
Hyperplanes
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Multiradial functions
Partial Differential Equations
Pointwise estimates
Signal,Image and Speech Processing
Sobolev spaces
Strauss inequality
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Summary:The paper gives sharp pointwise estimates for functions belonging to H ˙ s , p ( R N ) with radial symmetry in m blocks of variables, for m < s p < N . The estimates are formulated in terms of multiradial monomials. The form of the monomials depends on the structure of the group of block-radial symmetries and the distances of the given point to the hyperplanes in R N that contain the singular orbits of the group. For some exceptional set of parameters the logarithmic factor is needed. Weak continuity related to the estimates is also considered.
ISSN:1069-5869
1531-5851
1531-5851
DOI:10.1007/s00041-018-9593-7