On the Boundedness of Singular Integral Operators in Symmetric Spaces - Peleshenko, B. I. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We consider the integral convolution operators \(T_ε f\left( x \right) = \int\limits_{|x - y| > ε } {k\left( {x - y} \right)f\left( y \right)dy}\) 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 ε are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces.