Characterization of Functions from Spaces Defined on Terms of p-Integrability of Mean Oscillation
The paper is devoted to continuation of the study of classes of functions with condition on mean oscillation, started in A.N. Karapetyanrs, F.D.Kodzoeva. (Izvestya Vuzov. Severo-Kavkazskii region. Estestvennye Nauki. 2012. № 4. S. 5 – 8). That is, the spaces of functions with p-integrable (with weight) mean oscillation are studied. Problems of connectedness and prolongation for such functions are studied, sufficient conditions for a function to be from such spaces are obtained. As an application, we study boundedness of convolution operator and operator with homogeneous (–1) kernel in mentioned spaces on real line and half line correspondingly.