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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
DOI: https://doi.org/10.1090/S0002-9947-1989-0967312-4
MathSciNet review: 967312
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Abstract: We derive weighted Sobolev inequalities of the form ${\left \| f \right \|_{L_u^q}} \leq C{\left \| {\nabla f} \right \|_{L_v^p}}$, $f \in C_0^\infty ({{\mathbf {R}}^n})$, $1 < p \leq q < \infty$, 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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Article copyright: © Copyright 1989 American Mathematical Society