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Transactions of the American Mathematical Society

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On a convolution theorem for $ L(p,q)$ spaces


Author: A. P. Blozinski
Journal: Trans. Amer. Math. Soc. 164 (1972), 255-265
MSC: Primary 46E30; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9947-1972-0415293-1
MathSciNet review: 0415293
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Abstract: The principal result of this paper is a proof of the Convolution Theorem based on the definition of a convolution operator as presented by E. M. Stein and R. O'Neil. Closely related are earlier versions and special cases of the Convolution Theorem, which are $ L(p,q)$ analogues of an inequality of W. H. Young, given in papers by R. O'Neil, L. Y. H. Yap, R. Hunt, and B. Muckenhoupt and E. M. Stein.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Hunt, On $ L(p,q)$ spaces, Enseignement Math. (2) 12 (1966), 249-276. MR 36 #6921. MR 0223874 (36:6921)
  • [2] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. MR 33 #7779. MR 0199636 (33:7779)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0415293-1
Keywords: $ L(p,q)$ spaces, convolution operator, bilinear operator, Young's inequality
Article copyright: © Copyright 1972 American Mathematical Society

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