1 citations · 5 across the 25 of their papers we have counts for
27 papers
Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper addresses the existence of nontrivial solutions to a class of mixed local-nonlocal problems involving a mixed interpolated Hardy potential. We first establish a concentr…
Kernel estimates and weak (1,1)-boundedness of pseudo-differential operators on compact Lie groups
Duván Cardona, Rafik Yeghoyan, Michael Ruzhansky
Given a compact Lie group and its unitary dual , we establish the weak (1,1) continuity for pseudo-differential operators in the global Hörmander classes of order…
Spectral analysis, maximum principles and shape optimization for nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition opera…
Schatten-von Neumann classes of tensors of invariant operators
Julio Delgado, Liliana Posada, Michael Ruzhansky
In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tenso…
Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper aims to study the Brezis-Nirenberg type problem driven by the nonlinear superposition of operators of the form wher…
Besov and Triebel-Lizorkin spaces on homogeneous groups
Guorong Hu, David Rottensteiner, Michael Ruzhansky +1
This paper develops a theory of Besov spaces and Triebel-Lizorkin spaces on an arbitrary homogeneous group for the…
Classical inequalities for all Fourier matrix coefficients of and their applications
Vishvesh Kumar, Tapendu Rana, Michael Ruzhansky
In this article, we establish three fundamental Fourier inequalities: the Hausdorff-Young inequality, the Paley inequality, and the Hausdorff-Young-Paley inequality for -ty…
Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces: the critical case
Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
Subelliptic Nonlocal Brezis-Nirenberg Problems on Stratified Lie Groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-Δ_{\mathbb{G},…
- Fourier multipliers and Hausdorff-Young-Paley inequalities on Riemannian symmetric spaces of noncompact type
Tapendu Rana, Michael Ruzhansky
Our primary objective in this article is to establish Hörmander type Fourier multiplier theorems in the context of noncompact type Riemannian symmetric spaces…
Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and --boundedness of Fourier integral operators on compact manifolds
Duván Cardona, Julio Delgado, Michael Ruzhansky
We link Sogge's type -estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the -nuclearity of Fourier integral oper…
On fractional inequalities on metric measure spaces with polar decomposition
Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur
In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for is playing a key role in the proo…
Nearness and solvability of non-invariant equations on stratified groups
Marianna Chatzakou, Michael Ruzhansky, Nikos Yannakakis
We prove the well-posedness of the differential equation in the setting of a stratified group when the considered second-order differential operator can be…
Well-posedness for a class of pseudo-differential hyperbolic equations on the torus
Duvan Cardona, Julio Delgado, Michael Ruzhansky
In this paper we establish the well-posedness of the Cauchy problem for a class of pseudo-differential hyperbolic equations on the torus. The class considered here includes a space…
Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
On global solutions of heat equations with time-dependent nonlinearities on unimodular Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form on unimodular Lie groups when the differenti…
-bounds in Safarov pseudo-differential calculus on manifolds with bounded geometry
Santiago Gómez Cobos, Michael Ruzhansky
Given a smooth complete Riemannian manifold with bounded geometry and a linear connection on it (not necessarily a metric one), we prove the -boundedness of o…
Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds
Duván Cardona, Vishvesh Kumar, Michael Ruzhansky
In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We wi…
The weak (1,1) boundedness of Fourier integral operators with complex phases
Duván Cardona, Michael Ruzhansky
Let be a Fourier integral operator of order associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, S…
Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
Duván Cardona, Marianna Chatzakou, Julio Delgado +2
In this work we consider the semigroup for associated to an anharmonic oscillator of the form …
Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal +1
In this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian on the Heisenberg group with po…
Stein-Weiss inequality on non-compact symmetric spaces
Vishvesh Kumar, Michael Ruzhansky, Hong-Wei Zhang
Let be the Laplace-Beltrami operator on a non-compact symmetric space of any rank, and denote the bottom of its -spectrum as . In this paper, we provide a compre…
- estimates for subelliptic pseudo-differential operators on compact Lie groups
Duván Cardona, Julio Delgado, Vishvesh Kumar +1
We establish the --boundedness of subelliptic pseudo-differential operators on a compact Lie group . Effectively, we deal with the --bounds for operators in…
Semi-classical pseudo-differential operators on and applications
Linda N. A. Botchway, Marianna Chatzakou, Michael Ruzhansky
In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space . The current work is an extension of a previous work…