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Weighted Interpolation Inequalities and Embeddings in Rn

Published online by Cambridge University Press:  20 November 2018

R. C. Brown  and
D. B. Hinton
R. C. Brown
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350
D. B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300
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This paper is a continuation of [3] which initiated a systematic study of sufficient conditions for the weighted interpolation inequality of sum form, 1.1 to hold. Here ϕ, θ are non-negative functions of m, j, p, q, r, Ω is a bounded or unbounded domain in Rn, ∊ belongs to an interval Γ=(0, ∊0), u is in a certain Banach space E(Ω), and N, W, P are measurable real functions satisfying N≧ 0, W, P > 0, as well as additional conditions stated below. Finally the constant K does not depend on u although it may depend on the other parameters.

Keywords

26D1026D2054C25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 959 - 980
Copyright
Copyright © Canadian Mathematical Society 1990

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