Norm inequalities for potential-type operators in homogeneous spaces

Authors
Cascante, C Ortega, JM
Citation
C. Cascante et Jm. Ortega, Norm inequalities for potential-type operators in homogeneous spaces, MATH NACHR, 228, 2001, pp. 85-107
Citations number
22
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
228
Year of publication
2001
Pages
85 - 107
Database
ISI
SICI code
0025-584X(2001)228:<85:NIFPOI>2.0.ZU;2-W
Abstract
In this paper, we obtain a characterization of the positive Borel measures on a homogeneous space X, for which the trace inequality (integral (x)(I-Phi*f(x))(q) d mu (x))(1/q) less than or equal to C(integra l (x) f(x)(p) d sigma (x))(1/p) holds for any f greater than or equal to 0. Here I-Phi is a general potenti al type kernel, and 1 less than or equal to q <p < +infinity. The character ization is given in terms of a generalized Wolff's potential.