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Convolution of $ L(p,\,q)$ functions


Author: Anthony P. Blozinski
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
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Abstract: In the present paper, examples are given to show that the convolution theorem, which is the $ L(p,q)$ analogue of Young's 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 [Enhancements On Off] (What's this?)

  • [1] A. P. Blozinski, On translation-invariant operators, convolution operators and $ L(p,q)$ spaces, Ph.D. Thesis, Purdue University, Lafayette, Indiana, 1970.
  • [2] -, On a convolution theorem for $ L(p,q)$ spaces, Trans. Amer. Math. Soc. 164 (1972), 255-265. MR 0415293 (54:3383)
  • [3] L. Hörmander, Estimates for translation invariant operators in $ {L^p}$ spaces, Acta Math. 104 (1960), 93-140. MR 22 #12389. MR 0121655 (22:12389)
  • [4] R. A. Hunt, On $ L(p,q)$ spaces, Enseignement Math (2) 12 (1966), 249-276. MR 36 #6921. MR 0223874 (36:6921)
  • [5] N. W. Rickert, Convolution of $ {L^p}$ functions, Proc. Amer. Math. Soc. 18 (1967), 762-763. MR 35 #7136. MR 0216301 (35:7136)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288526-8
Keywords: $ L(p,q)$ spaces, convolution, convolution theorem, Young's inequality, translation invariant operator, locally compact group
Article copyright: © Copyright 1972 American Mathematical Society

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