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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The second author is supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 10XNF090); the third author is supported by National Natural Science Foundation of China (Grant No. 10871025)
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Liang, Y.Y., Liu, L.G. & Yang, D.C. An off-diagonal Marcinkiewicz interpolation theorem on Lorentz spaces. Acta. Math. Sin.-English Ser. 27, 1477–1488 (2011). https://doi.org/10.1007/s10114-011-0287-1
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DOI: https://doi.org/10.1007/s10114-011-0287-1