Related papers: $(p,q)$-Dominated Multilinear Operators and Lapres…
In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
This article sets forth results on the existence, positivity and boundedness of solutions for quasilinear elliptic systems involving p-Laplacian and q-Laplacian operators. The approach combines Schaefer's fixed point, comparison principle…
We introduce and study the class of unbounded DunfordPettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.
We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian with $1<q<p$. The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive…
In this work, we review and extend some well known results for the eigenvalues of the Dirichlet $p-$Laplace operator to a more general class of monotone quasilinear elliptic operators. As an application we obtain some homogenization results…
We study a new class of infinite-dimensional Lie algebras W_\infty(p,q) generalizing the standard W_\infty algebra, viewed as a tensor operator algebra of SU(1,1) in a group-theoretic framework. Here we interpret W_\infty(p,q) either as an…
An algebraic interpretation of the $q$-Meixner polynomials is obtained. It is based on representations of $\mathcal{U}_q(\mathfrak{su}(1,1))$ on $q$-oscillator states with the polynomials appearing as matrix elements of unitary…
We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…
In this paper, we study the mapping property form $L^p$ to $L^q$ of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schr\"odinger operators. Though the first half of the subject is studied in [4], we…
In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we…
The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…
The recent theorem by D. Luecking that finite rank Toeplitz-Bergman operators must be generated by a measure consisting of finitely many point masses is carried over to the many-dimensional case.
We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free…
An operator on an $l^{p}$-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich band-dominated operator is $\mathcal{P}$-Fredholm (which is…
We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we…
In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^{q}-L^{r}$ boundedness of…
We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a…
We give some new characterizations of strictly Lipschitz p-summing operators. These operators have been introduced in order to improve the Lipschitz p-summing operators. Therefore, we adapt this definition for constructing other classes of…
In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor…