On hypersingular integrals and anisotropic Bessel potential spaces. (English) Zbl 0558.42009
The purpose of this paper is to obtain a characterization of the anisotropic space of Bessel potentials, \(L^ p_{\alpha}\), \(\alpha >0\), \(1<p<\infty\), in terms of hypersingular integrals. The main result extends previous work by P. I. Lizorkin [Mat. Sb., Nov. Ser. 81(123) (1970), 79-91 (1969; Zbl 0198.188)] where the case of diagonal dilation matrices is considered.
Reviewer: M.Milman
MSC:
| 42B15 | Multipliers for harmonic analysis in several variables |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Citations:
Zbl 0198.188References:
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