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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Sobolev inequalities for products of powers
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by A. Eduardo Gatto and Richard L. Wheeden PDF
Trans. Amer. Math. Soc. 314 (1989), 727-743 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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