Related papers: $p$-regularity and weights for operators between $…

Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where…

For a given second-order linear elliptic operator $L$ which admits a positive minimal Green function, and a given positive weight function $W$, we introduce a family of weighted Lebesgue spaces $L^p(\phi_p)$ with their dual spaces, where…

This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the…

We define a p-norm in the context of quantum random variables, measurable operator-valued functions with respect to a positive operator-valued measure. This norm leads to a operator-valued L^p space that is shown to be complete. Various…

Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of…

Our principal result is the following. Let $X$ and $Y$ be Banach spaces, let $G$ be a locally compact abelian group, and let $K$ be an operator valued kernel defined on $G$ with values in the space of bounded linear operators from $X$ to…

We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these…

Let $(A,\mathscr{A},\mu)$ and $(B,\mathscr{B},\nu)$ be probability spaces, let $\mathscr{F}$ be a sub-$\sigma$-algebra of the product $\sigma$-algebra $\mathscr{A}\times\mathscr{B}$, let $X$ be a Banach space, and let $1< p,q< \infty$. We…

We study two weight norm inequalities for a vector-valued operator from a weighted $L^p(\sigma)$-space to mixed norm $L^q_{l^s}(\mu)$ spaces, $1<q<p$. We apply these results to the boundedness of Wolff's potentials.

Let $T$ be a bounded linear operator on $L^p$. We study the rate of growth of the norms of the powers of $T$ under resolvent conditions or Ces\`aro boundedness assumptions. Actually the relevant properties of $L^p$ spaces in our study are…

It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we investigate some…

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…

Let ${\mathcal P}$ be a family of probability measures on a measurable space $(S,{\mathcal A}).$ Given a Banach space $E,$ a functional $f:E\mapsto {\mathbb R}$ and a mapping $\theta: {\mathcal P}\mapsto E,$ our goal is to estimate…

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…

In this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the…

Smith et al. recently gave the sufficient and necessary conditions for the boundedness of Volterra type operators on Banach spaces of bounded analytic functions when the symbol functions are univalent. In this paper, we give the complete…

A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be $p_\tau$-bounded…

We study $l^{p}$ operator norms of weighted mean matrices using the approaches of Kaluza-Szeg\"o and Redheffer. As an application, we prove a conjecture of Bennett.

In this paper we characterize Birkhoff-James orthogonality of linear operators defined on a finite dimensional real Banach space $ \mathbb{X}. $ We also explore the symmetry of Birkhoff-James orthogonality of linear operators defined on $…

We study the operators T on the weighted space L^p commuting either with the right translations St or left translations P^+S_{-t} and we establish the existence of a symbol of T. We characterize completely the spectrum of St. We obtain a…