Related papers: R-boundedness of smooth operator-valued functions

In this paper, the authors establish the existence and boundedness of multilinear Littlewood--Paley operators on products of BMO spaces, including the multilinear $g$-function, multilinear Lusin's area integral and multilinear…

We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…

Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY is a subspace of Y+F for some finite-dimensional ``error'' F. In this paper, we study subspaces that are almost invariant under…

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

In this paper, we prove that the Cauchy integral operators (or Cauchy transforms) define continuous linear operators on the Smirnov classes for some certain domain with closed analytic boundary.

We introduce a weakened notion of norm attainment for bounded linear operators between Banach spaces which we call \emph{quasi norm attaining operators}. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is…

Let $\Omega\subset\mathbb{C}^n$ be a domain and $1 \leq q \leq n-1$ fixed. Our purpose in this article is to establish a general sufficient condition for the closed range of the Cauchy-Riemann operator $\bar\partial$ in appropriately…

Let $X$ be a vector lattice and $(E,\tau)$ be a locally solid vector lattice. An operator $T:X\to E$ is said to be $ob$-bounded if, for each order bounded set $B$ in $X$, $T(B)$ is topologically bounded in $E$. In this paper, we study on…

We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving…

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

We give an extension of Rubio de Francia's extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an $m$-(sub)linear operator…

For any non-Archimedean local field $\mathbb{K}$ and any integer $n \geq 1$, we show that the Taibleson operator admits a bounded $\mathrm{H}^\infty(\Sigma_\theta)$ functional calculus on the Bochner space $\mathrm{L}^p(\mathbb{K}^n,Y)$ for…

In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability…

Let $L = \Delta + V$ be a Schr\"odinger operator with a non-negative potential $V$ on a complete Riemannian manifold $M$. We prove that the vertical Littlewood-Paley-Stein functional associated with $L$ is bounded on $L^p(M)$ {\it if and…

We study linear operators $T$ on Banach spaces for which there exists a $C_0$-semigroup $(T(t))_{t\geq 0}$ such that $T=T(1)$. We present a necessary condition in terms of the spectral value 0 and give classes of examples where this can or…

We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.

We consider a class of bounded linear operators between Banach spaces, which we call operators with the Kato property, that includes the family of strictly singular operators between those spaces. We show that if $T:E\to F$ is a dense-range…

The paper deals with $L_p$-boundedness of the Hartley-Fourier convolutions operator and their applied aspects. We establish various new Young-type inequalities and obtain the structure of a normed ring in Banach space when equipping it with…

For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to…

As it was shown by Shen, the Riesz transforms associated to the Schr\"odinger operator $L=-\Delta + V$ are not bounded on $L^p(\mathbb{R}^d)$-spaces for all $p, 1<p<\infty$, under the only assumption that the potential satisfies a reverse…