Generalized Morrey regularity for parabolic equations with discontinuity data

Abstract

We obtain continuity in generalized parabolic Morrey spaces of sublinear integrals generated by the parabolic Calderón-Zygmund operators and its commutator with $VMO$ functions. The obtained estimates are used to study global regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations with discontinuous coefficients.

16 pages

References in corpus (1)

• Parabolic oblique derivative problem in generalized Morrey spaces

Cited by in corpus (4)

• Parabolic oblique derivative problem in generalized Morrey spaces
• The Dirichlet problem in a class of generalized weighted spaces
• Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
• Morrey meets Muckenhoupt: A note on Nakai's generalized Morrey spaces and applications