Abstract
We prove equivalence of sufficient conditions for boundedness of convolution integral operators in rearrangement-invariant spaces which were obtained in the articles of S. G. Kreīn, E. M. Semenov, and the author. The first of these conditions generalizes the Hardy–Littlewood–Sobolev condition and the second is a modification of the Hörmander condition.
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Kre\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{i} \);n S. G., Petunin Yu. I., and Semënov E. M., Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).
Peleshenko B. I., “To Hörmander's theorem on an integral convolution operator, ” in: Problems of Mathematical Analysis and Applied Problems of Mechanics [in Russian], Dnepropetrovsk, 1998, pp. 3–12.
Hörmander L., Estimates for Translation Invariant Operators in Lp Spaces [Russian translation], Izdat. Inostr. Lit., Moscow (1962).
Stein E. and Weiss G., Introduction to Harmonic Analysis on Euclidean Spaces [Russian translation], Mir, Moscow (1974).
Natanson I. P., The Theory of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1974).
Stepanov V. D., “On integral convolution operators, ” Dokl. Akad. Nauk SSSR, 243, No. 1, 45–48 (1978).
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Peleshenko, B.I. Sufficient Conditions for Boundedness of Convolution Operators in Rearrangement-Invariant Spaces. Siberian Mathematical Journal 42, 546–550 (2001). https://doi.org/10.1023/A:1010479327687
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DOI: https://doi.org/10.1023/A:1010479327687