A CHOICE OF SOBOLEV SPACES ASSOCIATED WITH ULTRASPHERICAL EXPANSIONS

被引：9

作者：

Betancor, Jorge J. ^{[1
]}

Farina, Juan C. ^{[1
]}

Rodriguez-Mesa, Lourdes ^{[1
]}

Testoni, Ricardo ^{[2
]}

Torrea, Jose L. ^{[3
,4
]}

机构：

[1] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Sta Cruz Teneri, Spain

[2] Univ Nacl Sur, Dept Matemat, RA-8000 Bahia Blanca, Buenos Aires, Argentina

[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[4] ICMAT CSIC UAM UCM UC3M, Madrid 28049, Spain

来源：

PUBLICACIONS MATEMATIQUES | 2010年 / 54卷 / 01期

关键词：

Sobolev spaces; ultraspherical expansions; MAXIMAL-FUNCTION; TRANSPLANTATION THEOREM; CONJUGATE EXPANSIONS; REGULARITY; SERIES;

D O I：

10.5565/PUBLMAT_54110_13

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss two possible definitions for Sobolev space associated with ultraspherical expansions. These definitions depend on the notion of higher order derivative. We show that in order to have an isomorphism between Sobolev and potential spaces, the higher order derivatives to be considered are not the iteration of the first order derivatives. Some discussions about higher order Riesz transforms are involved. Also we prove that the maximal operator for the Poisson integral in the ultraspherical setting is bounded on the Sobolev spaces.

引用

页码：221 / 242

页数：22

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