Vishvesh Kumar

activity

20212024

most citedStein-Weiss inequality on non-compact symmetric spaces

1 citations · 3 across the 12 of their papers we have counts for

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10 papers · 1 filter

math.AP2025

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 $A_{μ, p} u := \int_{[0, 1]} (- Δ)_{p}^{s} u d μ (s),$ wher…

math.AP2024

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…

math.AP2024

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 $e^{- t A_{k, ℓ}^{γ}}$ for $γ > 0$ associated to an anharmonic oscillator of the form $A_{k, ℓ} = (- Δ)^{ℓ} + ∣ x ∣^{2 k}$ …

math.AP2024

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 $L$ on the Heisenberg group $H^{n}$ with po…

math.AP2023★ 1 cited

Stein-Weiss inequality on non-compact symmetric spaces

Vishvesh Kumar, Michael Ruzhansky, Hong-Wei Zhang

Let $Δ$ be the Laplace-Beltrami operator on a non-compact symmetric space of any rank, and denote the bottom of its $L^{2}$ -spectrum as $- ∣ ρ ∣^{2}$ . In this paper, we provide a compre…

math.AP2023

$L^{p}$ - $L^{q}$ estimates for subelliptic pseudo-differential operators on compact Lie groups

Duván Cardona, Julio Delgado, Vishvesh Kumar +1

We establish the $L^{p}$ - $L^{q}$ -boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$ . Effectively, we deal with the $L^{p}$ - $L^{q}$ -bounds for operators in…

Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order

Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds

Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations

Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order

Stein-Weiss inequality on non-compact symmetric spaces

Lp-Lq estimates for subelliptic pseudo-differential operators on compact Lie groups

$L^{p}$ - $L^{q}$ estimates for subelliptic pseudo-differential operators on compact Lie groups