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We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…
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…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex-valued potentials in dimensions one, two and three.
In this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{\rho,\delta}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{\rho,\delta}^m) \subset…
Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…
Inspired by our previous work on the boundedness of Toeplitz operators, we introduce weak BMO and VMO type conditions, denoted by BWMO and VWMO, respectively, for functions on the open unit disc of the complex plane. We show that the…
We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…
In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.
In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichm\"uller geodesic trajectories.The main tool is quantitative nondivergence of…
This paper is devoted to studying some mixed radial-angular integrabilities for various types of Hausdorff operators and commutators
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…
We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition…
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…
In this article, we establish some conditions for the boundedness of fractional integral operators on the vanishing generalized weighted Morrey spaces. We also investigate corresponding commutators generated by BMO functions.
It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…
In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund operators ($\alpha=0$) and generated by fractional integral operator ($\alpha>0$) on…