On a convolution theorem for $L(p,q)$ spaces
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- by A. P. Blozinski PDF
- Trans. Amer. Math. Soc. 164 (1972), 255-265 Request permission
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. OβNeil. 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. OβNeil, L. Y. H. Yap, R. Hunt, and B. Muckenhoupt and E. M. Stein.References
- Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249β276. MR 223874
- B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17β92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9
- Richard OβNeil, Convolution operators and $L(p,\,q)$ spaces, Duke Math. J. 30 (1963), 129β142. MR 146673
- Leonard Y. H. Yap, Some remarks on convolution operators and $L(p,\,q)$ spaces, Duke Math. J. 36 (1969), 647β658. MR 249943
Additional Information
- © Copyright 1972 American Mathematical Society
- 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