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calderón—zygmund integrals

Proceedings of the Edinburgh Mathematical Society (1)

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Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data
Part of
Vagif S. Guliyev, Lubomira G. Softova
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 1 / February 2015

Published online by Cambridge University Press:

10 December 2014, pp. 199-218
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We prove continuity in generalized parabolic Morrey spaces of sublinear operators generated by the parabolic Calderón—Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. As a consequence, we obtain a global -regularity result for the Cauchy—Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation (VMO) coefficients.