The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions

DOI10.1016/j.jfa.2017.04.013OpenAlexW2557639060MaRDI QIDQ2357094

Raffaele Carlone, Lorenzo Tentarelli, Alberto Fiorenza

Publication date: 19 June 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.08503

zbMATH Keywords

Volterra integral equationssingular kernelsVolterra functionsSonine kernels

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fractional derivatives and integrals (26A33) Integral operators (47G10) Singular integral equations (45E99) Integral transforms, operational calculus (44A99)

Related Items

The point-like limit for a NLS equation with concentrated nonlinearity in dimension three, Global solutions to the non-local Navier-Stokes equations, Stability analysis for a class of anomalous diffusion involving impulsives and nonlinear pertubations, Fundamental solutions and decay of fully non-local problems, Stability of the standing waves of the concentrated NLSE in dimension two, Complete ionization for a non-autonomous point interaction model in \(\mathrm{d}=2\), A general review on the NLS equation with point-concentrated nonlinearity, Well–posedness of the three–dimensional NLS equation with sphere–concentrated nonlinearity, Stability and regularity in inverse source problem for generalized subdiffusion equation perturbed by locally Lipschitz sources, A non-local in time telegraph equation, Blow-up for the pointwise NLS in dimension two: absence of critical power, Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one, Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity, Emergence of Time-Dependent Point Interactions in Polaron Models, Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Volterra functions and Ramanujan integrals
• Hitchhiker's guide to the fractional Sobolev spaces
• Variable Lebesgue spaces. Foundations and harmonic analysis
• The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit
• Functional spaces for the theory of elliptic partial differential equations. Transl. from the French by Reinie Erné
• Weighted generalized Hölder spaces as wellposedness classes for Sonine integral equations
• Abel integral equations. Analysis and applications
• Existence and uniqueness for nonlinear singular integral equations used in fluid mechanics
• A formula for the Boyd indices in Orlicz spaces
• Blow-up solutions for the Schrödinger equation in dimension three with a concentrated non\-linearity.
• The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity
• Grenzordnungen von Operatoren-Idealen. II
• The point-like limit for a NLS equation with concentrated nonlinearity in dimension three
• Hölder and locally Hölder Continuous Functions, and Open Sets of Class C^k, C^{k,lambda}
• A Model Equation for Viscoelasticity with a Strongly Singular Kernel
• Fractional Integration in Orlicz Spaces
• Remark to history of fractional derivatives on complex plane: Sonine-Letnikov and Nishimoto derivatives
• Fractional Integration in Orlicz Spaces. I
• Two-dimensional Time-dependent Point Interactions
• Equivalent Norms for Sobolev Spaces
• A class of nonlinear Schrödinger equations with concentrated nonlinearity