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On the Boundedness of Singular Integral Operators in Symmetric Spaces

Authors:	B. I. Peleshenko

Affiliation:	(1) Dnepropetrovsk Agricultural University, Dnepropetrovsk

Abstract:	We consider the integral convolution operators $T_varepsilon fleft( x right) = intlimits_{\|x - y\| > varepsilon } {kleft( {x - y} right)fleft( y right)dy}$ 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} are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces.

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