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Transactions of the American Mathematical Society

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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
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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.


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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

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