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| Let (X,u) be a measure space. In thispaper, using some ideas from L. Grafakos and N. Kalton, the authorsestablish an off-diagonal Marcinkiewicz interpolation theorem for aquasilinear operator T in Lorentz spaces Lp,q(X) with p,q∈(0,∞], which is a corrected version of Theorem1.4.19 in [L. Grafakos, Classical Fourier Analysis, Second Edition,Graduate Texts in Math., No. 249, Springer, New York, 2008] andwhich, in the case that T is linear or nonnegative sublinear, p∈[1,∞)and q∈[1,∞), was obtained by E. M. Steinand G. 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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