Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multivariate rearrangements and Banach function spaces with mixed norms


Author: A. P. Blozinski
Journal: Trans. Amer. Math. Soc. 263 (1981), 149-167
MSC: Primary 46E30; Secondary 46M35
DOI: https://doi.org/10.1090/S0002-9947-1981-0590417-X
MathSciNet review: 590417
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Multivariate nonincreasing rearrangement and averaging functions are defined for functions defined over product spaces. An investigation is made of Banach function spaces with mixed norms and using multivariate rearrangements. Particular emphasis is given to the $ L(P,Q;\ast)$ spaces. These are Banach function spaces which are in terms of mixed norms, multivariate rearrangements and the Lorentz $ L(p,g)$ spaces. Embedding theorems are given for the various function spaces. Several well-known theorems are extended to the $ L(P,Q;\ast)$ spaces. Principal among these are the Strong Type (Riesz-Thorin) Interpolation Theorem and the Convolution (Young's inequality) Theorem.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E30, 46M35

Retrieve articles in all journals with MSC: 46E30, 46M35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0590417-X
Keywords: Multivariate rearrangements, averaging operators, Banach function spaces, Lorentz $ L(p,q)$ spaces, mixed norm spaces
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society