On the Boundedness of Singular Integral Operators in Symmetric Spaces - Peleshenko, B. I. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We consider the integral convolution operators \(T_ε f( x ) = _|x - y| > ε k( x - y )f( y )dy\) 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.