arXiv subjects
Publications and source records attributed to M. N. Omarova.
In this paper, we obtain the necessary and sufficient conditions for the weak/strong boundedness of the Calderón-Zygmund operators in generalized weighted Orlicz-Morrey spaces. We also study the boundedness of the commutators of Calderón-Zygmund operators on these spaces. Moreover, the boundedness of Calderón-Zygmund operators in the vector-valued setting is given.
In this paper, we will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the generalized weighted Morrey spaces $M^{Φ,φ}_{w}(\mathbb{R}^n)$. We study the boundedness of intrinsic square functions including the Lusin area integral, Littlewood-Paley $\mathrm{g}$-function and $\mathrm{g}_λ^{*}$ -function and their commutators on vector-valued generalized weighted Morrey spaces $M^{Φ,φ}_{w}(l_2)$. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on $φ(x,r)$ without assuming any monotonicity property of $φ(x,r)$ on $r$.