An off-diagonal Marcinkiewicz interpolation theorem on Lorentz spaces

作者：Liang, Yi Yu; Liu, Li Guang; Yang, Da Chun^*

来源：Acta Mathematica Sinica-English Series, 2011, 27(8): 1477-1488.

DOI：10.1007/s10114-011-0287-1

• Quasilinear operator
• Marcinkiewicz interpolation theorem
• Lorentz space
• restricted weak type estimate

Let (X, A mu) 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 a (0,a], 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 a [1,a) and q a [1,a), was obtained by Stein and Weiss [Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971].

• 出版日期2011-8
• 单位中国人民大学; 北京师范大学