Related papers: The maximal regularity operator on tent spaces

We prove uniform $L^p$ bounds for multilinear operators which are given by multipliers whose symbols are singular on a one dimensional subspace. The novelty is that these bounds are uniform in the choice of the subspace.

The present paper is the continuation of work \cite{XC}, devoted to extending it to a critical functional framework which is not related to the energy space. Employing the special dissipative structure of the non-conservative viscous…

For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…

In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal $\ell^p$-regularity in…

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calder\'on commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the…

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…

We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…

The present paper is devoted to the study of the well-posedness issue for the density-dependent Euler equations in the whole space. We establish local-in-time results for the Cauchy problem pertaining to data in the Besov spaces embedded in…

In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…

We study resolvent estimates and maximal regularity of the Stokes operator in $L^q$-spaces with exponential weights in the axial directions of unbounded cylinders of $\R^n,n\geq 3$. For a straight cylinder we use exponential weights in the…

We prove a weighted norm inequality for the maximal Bochner--Riesz operator and the associated square-function. This yields new $L^p(R^d)$ bounds on classes of radial Fourier multipliers for $p\ge 2+4/d$ with $d\ge 2$, as well as space-time…

In this paper we present an abstract maximal $L^p$-regularity result up to $T = \infty$, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional,…

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces $L^{p,q}(\mathfrak{X})$ in the context of certain non-doubling metric measure spaces $\mathfrak{X}$. The special class of…

Operators such as Carleson operator are known to be bounded on $L^p$ for all $1<p<\infty$, but not from $L^1$ to weak-$L^1$ and from $H^p$ to $L^p$ for each $0<p\leq 1$, the object of this article is to give a estimate for all $0<p<\infty$.…

We discuss Lebesgue spaces $\mathcal{L}^p([a,b],E)$ of Lusin measurable vector-valued functions and the corresponding vector spaces $AC_{L^p}([a,b],E)$ of absolutely continuous functions. These can be used to construct Lie groups…

We study the maximal regularity problem for abstract time-fractional Schr\"odinger equations $\partial_t^\alpha(u-u_0) -\mathrm{i} A u=f$, with a fractional derivative $\partial_t^\alpha$ of order $\alpha \in (0,1)$. We assume that $A$ is a…

We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are…

In this paper we establish $L^p$ boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein-Uhlenbeck…

We study the maximal operator on the variable exponent H\"older spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annular decay property. Let us stress that there are no…