Related papers: On Stein's extension operator preserving Sobolev-M…

Let $L^{m,p}(\R^n)$ be the Sobolev space of functions with $m^{th}$ derivatives lying in $L^p(\R^n)$. Assume that $n< p < \infty$. For $E \subset \R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in…

Using the Cauchy-Riemann operator, we characterize $Q_K$ spaces, Besov spaces and analytic Morrey spaces in terms of pseudoanalytic extensions of primitive functions. Our results are also true on some classical Banach spaces, such as the…

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…

Let $L^{m,p}(\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\R^n)$, and assume that $p>n$. For $E \subset \R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \in L^{m,p}(\R^n)$.…

In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz-Morrey spaces with variable exponent.

Let $\Omega \subseteq \mathbb{R}^d$ be open and $D\subseteq \partial\Omega$ be a closed part of its boundary. Under very mild assumptions on $\Omega$, we construct a bounded Sobolev extension operator for the Sobolev space $\mathrm{W}^{k ,…

We introduce grand Morrey spaces and establish the boundedness of Hardy--Littlewood maximal, Calder\'on--Zygmund and potential operators in these spaces. In our case the operators and grand Morrey spaces are defined on quasi-metric measure…

We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…

In this paper, we provide the boundedness property of the Riesz transforms associated to the Schr\"odinger operator $\mathcal{L}=-\Delta + \mathbf{V}$ in a new weighted Morrey space which is the generalized version of many previous Morrey…

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…

In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the…

We prove an endpoint version of the Stein-Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein's estimate on oscillatory integrals of…

We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…

In this paper we introduce a class of generalized Morrey spaces associated with Schr\"odinger operator $L=-\Delta+V$. Via a pointwise estimate, we obtain the boundedness of the operators $V^{\beta_{2}}(-\Delta+V)^{-\beta_{1}}$ and their…

Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected $C^2$-manifold without boundary. The proof combines a…

In our companion paper (S.N. Chandler Wilde, D.P. Hewett, A. Moiola, Sobolev spaces on non-Lipschitz subsets of $\mathbb{R}^n$ with application to boundary integral equations on fractal screens, 2016) we studied a number of different…

We discuss a few old results concerning embedding theorems for Campanato and Sobolev-Morrey spaces adapting the formulations to the case of domains of class $C^{0,\gamma}$, and we present more recent results concerning the extension of…

The classical McShane-Whitney extension theorem for Lipschitz functions is refined by showing that for a closed subset of the domain, it remains valid for any interval of the real line. This result is also extended to the setting of locally…

The continuity of the Nemytskii operator between Orlicz-Sobolev spaces is investigated. Natural Orlicz-Sobolev versions of classical results for standard Sobolev are established. The results presented not only extend the latter, but also…

In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…