An off-diagonal Marcinkiewicz interpolation theorem on Lorentz spaces |
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Authors: | Yi Yu Liang Li Guang Liu Da Chun Yang |
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Institution: | [1]School of Mathematical Sciences, Beijing Normal University,Laboratory of Mathematics and Corr~plex Systems, Ministry of Education, Beijing 100875, P. R. China [2]Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, P. R. China [3]School of Mathematical Sciences, Beijing Normal University,Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China |
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Abstract: | Let (X, μ) be a measure space. In this paper, using some ideas from Grafakos and Kalton, the authors establish an off-diagonal Marcinkiewicz
interpolation theorem for a quasilinear operator T in Lorentz spaces L
p,q
(X) with p, q ∈ (0,∞], which is a corrected version of Theorem 1.4.19 in Grafakos, L.: Classical Fourier Analysis, Second Edition, Graduate
Texts in Math., No. 249, Springer, New York, 2008] and which, in the case that T is linear or nonnegative sublinear, p ∈ 1,∞) and q ∈ 1,∞), was obtained by Stein and Weiss Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press,
Princeton, N.J., 1971]. |
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Keywords: | Quasilinear operator Marcinkiewicz interpolation theorem Lorentz space restricted weak type estimate |
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