Global Regularity in Generalized Morrey Spaces of Solutions to Nondivergence Elliptic Equations with VMO Coefficients

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

“…We will also investigate the boundedness of fractional multilinear integral operators with rough kernels T A 1 ;A 2 ;:::;A k ;˛o n the generalized weighted Nikolskii-Morrey spaces, see for example, [30]. These results may be applicable to some problems of partial differential equations; see for example [6,7,19,20,26,28,30,43].…”

Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients

“…Since (1) < ε then Lemma 5.2 ensures the validity of the hypotheses of Lemma 5.1 for the sets (22) and (23). Thus, we get by (25) {(x, t) ∈ Q r : M(|Du| 2 ) > λ 2…”

“…It ensures the validity in of some natural properties of geometric and functional analysis such as W 1,p -extension, non-tangential accessibility of the boundary, measure density condition, the Poincaré inequality and so on. We refer the reader to the works of Kenig and Toro [23], Toro [32] and the references therein for further details. In particular, a domain which is sufficiently flat in the sense of Reifenberg is also Jones flat.…”

Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces

“…In the case of the classical Morrey spaces we refer for instance to [28] and [32], in the case of generalized Morrey spaces to [35] (where some monotonicity assumptions were imposed on the function ϕ, but on the other hand an anisotropic case was admitted) and to [14,15] (where no monotonicity assumptions on ϕ were imposed, including an anisotropic case [15]), where other references may be also found. The results for commutators in the setting of Orlicz-Morrey spaces in this paper are new even in the case of non-vanishing spaces.…”