Related papers: Fractional Vector-Valued Littlewood-Paley-Stein Th…

In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of…

In this paper, we study vector--valued elliptic operators of the form $\mathcal{L}f:=\mathrm{div}(Q\nabla f)-F\cdot\nabla f+\mathrm{div}(Cf)-Vf$ acting on vector-valued functions $f:\mathbb{R}^d\to\mathbb{R}^m$ and involving coupling at…

We study the functional calculus for operators of the form $f_h(P(h))$ within the theory of semiclassical pseudodifferential operators, where $\{f_h\}_{h\in (0,1]}\subset C^\infty_c(\mathbb{R})$ denotes a family of $h$-dependent functions…

In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional…

For certain non compact Riemannian manifolds with ends, we obtain Littlewood-Paley type estimates on (weighted) Lp spaces, using the usual square function defined by a dyadic partition.

We investigate a class of nonlinear time-space fractional Schr\"{o}dinger equations with nonlocal effects in both time and space. The time derivative is of Achar type, and the space operator is a $\phi(-\Delta)$-type operator defined via a…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered…

We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie…

We present a polynomiality property of the Littlewood-Richardson coefficients c_{\lambda\mu}^{\nu}. The coefficients are shown to be given by polynomials in \lambda, \mu and \nu on the cones of the chamber complex of a vector partition…

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…

Schr\'{o}dinger's equation with distributional $\delta$, or $\delta'$ potentials has been well studied in the past. There are challenges in simultaneously addressing some of the inherent issues of the system: The functional operator cannot…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"older continuous condition. In this article, the authors first introduce the variable weak Hardy space on $\mathbb R^n$,…

We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity…

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…

Starting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an applications we find…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and…

We consider a semigroup of operators in the Banach space $C_b(H)$ of uniformly continuous and bounded functions on a separable Hilbert space $H$. In particular, we deal with semigroups that are related to solution of stochastic PDEs in $H$…

In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs…

We show how H\"older estimates for Feller semigroups can be used to obtain regularity results for solutions to the Poisson equation $Af=g$ associated with the (extended) infinitesimal generator $A$ of a Feller process. The regularity of $f$…