Convolution of $L(p, q)$ functions
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- by Anthony P. Blozinski PDF
- Proc. Amer. Math. Soc. 32 (1972), 237-240 Request permission
Abstract:
In the present paper, examples are given to show that the convolution theorem, which is the $L(p,q)$ analogue of Youngโs inequality for the ${L^p}$ spaces, is best possible. This result is then used to obtain a theorem about bounded linear translation invariant operators between two $L(p,q)$ spaces.References
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A. P. Blozinski, On translation-invariant operators, convolution operators and $L(p,q)$ spaces, Ph.D. Thesis, Purdue University, Lafayette, Indiana, 1970.
- A. P. Blozinski, On a convolution theorem for $L(p,q)$ spaces, Trans. Amer. Math. Soc. 164 (1972), 255โ265. MR 415293, DOI 10.1090/S0002-9947-1972-0415293-1
- Lars Hรถrmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93โ140. MR 121655, DOI 10.1007/BF02547187
- Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249โ276. MR 223874
- Neil W. Rickert, Convolution of $L^{p}$ functions, Proc. Amer. Math. Soc. 18 (1967), 762โ763. MR 216301, DOI 10.1090/S0002-9939-1967-0216301-7
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 237-240
- MSC: Primary 44.25
- DOI: https://doi.org/10.1090/S0002-9939-1972-0288526-8
- MathSciNet review: 0288526