摘要
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 ￡ [l,∞）, was obtained by Stein and Weiss [Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971].
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 ￡ [l,∞）, was obtained by Stein and Weiss [Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971].
基金
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）
