Related papers: Fractional operators on weighted Morrey spaces
We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity of the corresponding integral operator in H\"{o}lder spaces, is actually also necessary in…
We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spaces of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces…
In this paper we prove the sharp boundedness for a fractional type operator given by a kernel that satisfy a $L^{\alpha,r'}$-H\"ormander conditions and a fractional size condition, where $0<\alpha<n$ and $1< r'\leq \infty$. To prove this…
The Hardy operator is not bounded on the space of integrable functions on the positive half-line and its discrete counterpart on summable sequences. we introduce a modified Hardy operator obtained by subtracting a natural corrective term,…
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…
Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct…
We prove that for certain positive operators $T$, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant $D>1$, depending only on the dimension $n$, such that the two weight norm inequality…
In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators…
We provide a general condition on the kernel of an integro-differential operator so that its associated quadratic form satisfies a coercivity estimate with respect to the $H^s$-seminorm.
By a reduction method, the limiting weak-type behaviors of factional maximal operators and fractional integrals are established without any smoothness assumption on the kernel, which essentially improve and extend previous results. As a…
In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which…
We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by…
Let $ R $ be a rational map. We are interesting in the dynamic of the Ruelle operator on suitable spaces of differentials. In particular the necessary and sufficient conditions (in terms of convergence of sequences of measures) of existence…
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…
The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation…
In this paper, we investigated the boundedness of multilinear fractional strong maximal operator $\mathcal{M}_{\mathcal{R},\alpha}$ associated with rectangles or related to more general basis with multiple weights…
We consider local "complementary" generalized Morrey spaces ${\dual \cal M}_{\{x_0\}}^{p(\cdot),\om}(\Om)$ in which the $p$-means of function are controlled over $\Om\backslash B(x_0,r)$ instead of $B(x_0,r)$, where $\Om \subset \Rn$ is a…
We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained…