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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sobolev inequalities for products of powers


Authors: A. Eduardo Gatto and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 314 (1989), 727-743
MSC: Primary 26D10; Secondary 46E35
MathSciNet review: 967312
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Abstract: We derive weighted Sobolev inequalities of the form $ {\left\Vert f \right\Vert _{L_u^q}} \leq C{\left\Vert {\nabla f} \right\Vert _{L_v^p}}$, $ f \in C_0^\infty ({{\mathbf{R}}^n})$, $ 1 < p \leq q < \infty $, for classes of weight functions $ u$, $ v$ which include $ v$'s that are a finite product of certain power weights times an $ {A_p}$ function.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0967312-4
PII: S 0002-9947(1989)0967312-4
Article copyright: © Copyright 1989 American Mathematical Society