On the Boundedness of Singular Integral Operators in Symmetric Spaces

Authors

  • B. I. Peleshenko

Abstract

We consider the integral convolution operators Tεf(x)=|xy|>εk(xy)f(y)dy defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we establish necessary and sufficient conditions under which the operators {T ε} are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces.

Published

25.07.2000

Issue

Section

Short communications

How to Cite

Peleshenko, B. I. “On the Boundedness of Singular Integral Operators in Symmetric Spaces”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 7, July 2000, pp. 988-93, https://umj.imath.kiev.ua/index.php/umj/article/view/4500.