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Proceedings of the American Mathematical Society

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A note on Sobolev algebras


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 29 (1971), 205-207
MSC: Primary 46.38
DOI: https://doi.org/10.1090/S0002-9939-1971-0275148-7
MathSciNet review: 0275148
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Abstract: Sufficient conditions are given for the Sobolev space $ L_w^p = \{ f \in {L^p}({E^n}):{\mathfrak{F}^{ - 1}}(\hat f(\xi )w(\xi )) \in {L^p}\} $ to form an algebra under pointwise multiplication, when $ 1 \leqq p \leqq 2$. The conditions are verified for some examples.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0275148-7
Keywords: Sobolev spaces, $ {L^p}$ multipliers, Sobolev algebras
Article copyright: © Copyright 1971 American Mathematical Society

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