Related papers: Sobolev spaces, Lebesgue points and maximal functi…

In this article we investigate $L^p$ boundedness of the spherical maximal operator $\mathfrak{m}^\alpha$ of (complex) order $\alpha$ on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, which was introduced and studied by El Kohen. We…

We explore the consequences for the boundedness properties of averaging and maximal averaging operators, of the following local comparabiliity condition for measures: Intersecting balls of the same radius have comparable sizes. Since in…

In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesgue and generalized Morrey spaces as special cases. Further,…

We study the convergence and divergence of the wavelet expansion of a function in a Sobolev or a Besov space from a multifractal point of view. In particular, we give an upper bound for the Hausdorff and for the packing dimension of the set…

We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…

Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of…

In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb{R}^d$, on the…

We study the operator $\mathcal{A}$ of multiplication by an independent variable in a matrix Sobolev space $W^2(M)$. In the cases of finite measures on $[a,b]$ with $(2\times 2)$ and $(3\times 3)$ real continuous matrix weights of full rank…

We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…

In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of…

This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…

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…

Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…

We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the "inclusion" between operators becomes a full equality.

Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point…

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$ and let $w$ be a positive function on $X$ such that $w\in W^{1,s}(X,\mu)$ and $\log w\in W^{1,t}(X,\mu)$ for some $s>1$ and $t>s'$. In the…

We propose a survey on composition operators in classical Sobolev spaces. We mention results obtained in 2019, on the continuity of such operators.

We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a…

We give an intrinsic characterization of the restrictions of Sobolev, Triebel-Lizorkin and Besov spaces to regular subsets of $R^n$ via sharp maximal functions and local approximations.

We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with $L^1$ data. We also find the optimal target spaces for such embeddings, which in dimension 2 could be…