The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L p (ν) (0 < p < r < ∞) which satisfies a vector-valued norm inequality

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...

Aim of this paper is to study the parabolic Volterra equation u(t) + (b ∗Au)(t) = (QB)(t), t ≥ 0, on a separable Hilbert space. Throughout this work the operator −A is assumed to be a differential operator like the Laplacian, the elasticity operator, or the Stokes operator. The random disturbance Q1/2BH is modeled to be a system independent vector valued fractional Brownian motion with Hurst pa...

Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication to vector model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that product $A_\Phi A_\Psi$ itself operator.

In this paper, we prove the sharp function inequality for the multilinear commutator related to the singular integral operator with variable Calderón-Zygmund kernel. By using the sharp inequality, we obtain the Lnorm inequality for the multilinear commutator. 2000 Mathematics Subject Classification: 42B20, 42B25.

After the pioneer work of Calderón and Zygmund in the 50’s, the systematic study of singular integrals has become a corner stone in harmonic analysis with deep implications in mathematical physics, partial differential equations and other mathematical disciplines. Subsequent generalizations of Calderón-Zygmund theory have essentially pursued two lines. We may either consider more general domain...

Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discre...

In this paper, we combine the fractional ψ − $$ \psi - hyperholomorphic function theory with calculus respect to another function. As a main result, Borel–Pompeiu type formula related Fueter operator vector-valued is proved.