Hardy inequalities on constant-order noncommutative Vilenkin groups

Kassymov, Aidyn; Velasquez-Rodriguez, J. P

doi:10.48550/arxiv.2208.03495

Cited by 1 publication

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“…In [Wei07], the almost everywhere convergence of Banach space-valued Vilenkin-Fourier series is investigated. In [KaV22], Hardy inequalities were explored. Multiplier theory was investigated in [OnQ89].…”

Section: Locally Compact Vilenkin Groupsmentioning

confidence: 99%

Boundedness of H ∞ Functional Calculus of Hodge-Dirac Operators

Arhancet¹,

Kriegler

2022

Lecture Notes in Mathematics

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For any non-archimedean local field K and any integer n ⩾ 1, we show that the Taibleson operator admits a bounded H ∞ (Σ θ ) functional calculus for any angle θ > 0 on the Banach space L p (K n ), where Σ θ = {z ∈ C * : | arg z| < θ} and 1 < p < ∞, and even a bounded Hörmander functional calculus of order 3 2 (with striking contrast to the Euclidean Laplacian on R n ). In our study, we explore harmonic analysis on locally compact Spector-Vilenkin groups establishing the R-boundedness of a family of convolution operators. Our results enhance the understanding of functional calculi of operators acting on L p -spaces associated to totally disconnected spaces and have implications for the maximal regularity of the fundamental evolution equations associated to the Taibleson operator, relevant in various physical models. Contents 1 Introduction 1 2 Preliminaries 5 3 Locally compact Spector-Vilenkin groups and radial functions 10 4 Maximal inequalities 15 5 R-boundedness of some family of convolution operators 17 6 Application to functional calculus 20 Bibliography 27 2020 Mathematics subject classification: 46S10, 47S10, 11S80.

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Section: Locally Compact Vilenkin Groupsmentioning

confidence: 99%