Non-tangential control of the solutions to deterministic and stochastic parabolic Cauchy problems

We study a (stochastic) parabolic Cauchy problem. We first prove that we have a non-tangential control of the solution of the deterministic parabolic Cauchy problem by the tent space norm of the gradient of the solution. This is done by showing boundedness results for several maximal regularity operators and by developing energy solutions in L^2...

Maximal functions, factorization, and the R-boundedness of integral operators

We generalize a recent result on the ℓs-boundedness of a family of integral operators from the weighted vector-valued Lp(Rd,w;Lq(Ω)) setting to the weighted vector-valued Lp(Rd,w;X) setting for a large class of Banach function spaces X. For this we first extensively study the first part of an unpublished manuscript on the factorization of ℓ2...