<i>L</i> <i>p</i> -<i>L</i> <i>q</i> Boundedness of <i>(k, a)</i>-Fourier Multipliers with Applications to Nonlinear Equations
Vishvesh Kumar, Michael Ruzhansky
Abstract
Abstract The $(k,a)$-generalised Fourier transform is the unitary operator defined using the $a$-deformed Dunkl harmonic oscillator. The main aim of this paper is to prove $L^p$-$L^q$ boundedness of $(k, a)$-generalised Fourier multipliers. To show the boundedness, we first establish Paley inequality and Hausdorff–Young–Paley inequality for $(k, a)$-generalised Fourier transform. We also demonstrate applications of obtained results to study the well-posedness of nonlinear partial differential equations.
Topics & Concepts
MathematicsFourier transformUnitary stateMultiplier (economics)Nonlinear systemPure mathematicsMathematical analysisHarmonic analysisMacroeconomicsPolitical scienceQuantum mechanicsPhysicsLawEconomicsMathematical Analysis and Transform MethodsAdvanced Harmonic Analysis ResearchAdvanced Mathematical Physics Problems