Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral operator, acting on LpX(R ) with p ∈ (1,∞). Moreover, replacing equality by a linear equivalence, this is fo...

To characterize the regularity of distribution-path dependent SDEs in initial distribution which varies as probability measure on path space, we introduce intrinsic and Lions derivatives for measures Banach spaces, prove chain rule derivative Banach-valued random variables. By using Malliavin calculus, establish Bismut type formula functional solutions to with drifts. When noise term is also so...

We consider vector-valued random fields on a general index set in R and show the existence of continuous modifications if some Kolmogorov type condition is satisfied. Furthermore, we prove an extension result for Hölder continuous vector valued mappings. 2000 Mathematics Subject Classification: 60G60, 46E40.

We show that the duals of Banach algebras scalar-valued bounded holomorphic functions on open unit ball BE a space E lack weak⁎-strongly exposed points. Consequently, we obtain some an arbitrary have Daugavet property which extends observation P. Wojtaszczyk [56]. Moreover, present new denseness result by proving set norm-attaining vector-valued dual is dense provided its predual has metric π-p...

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation unbounded subsets, also applying an extension positive linear operators’ result. The domain is Banach lattice continuous real-valued functions a compact subset or Lν1 space, where ν determinate measure closed set. existence uniqueness operator soluti...

Motivated by the work of George A. Anastassiou in [George A. Anastassiou, Ostrowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312–329], we derive some Landau type inequalities for Banach space valued functions without assuming the boundary conditions.

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.