Wavelets, Sobolev multipliers, and application to Schrödinger type operators with nonsmooth potentials

DOI10.1155/2013/193420zbMath1298.42039arXiv1301.0696OpenAlexW2112080381WikidataQ58915499 ScholiaQ58915499MaRDI QIDQ2016709

Pengtao Li, Yue Ping Zhu, Qi-Xiang Yang

Publication date: 20 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0696

zbMATH Keywords

waveletsSobolev spacespointwise multipliers

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characterization of multiplier spaces with Daubechies wavelets
• The dyadic structure and atomic decomposition of \(Q\) spaces in several real variables
• The Schrödinger operator on the energy space: Boundedness and compactness criteria
• Predual spaces for \(Q\) spaces
• Characterizations of localized BMO(\({\mathbb R}^n\)) via commutators of localized Riesz transforms and fractional integrals associated to Schrödinger operators
• Homothetic variant of fractional Sobolev space with application to Navier-Stokes system
• A new class of function spaces connecting Triebel--Lizorkin spaces and \(Q\) spaces
• New Besov-type spaces and Triebel-Lizorkin-type spaces including \(Q\) spaces
• Localized BMO and BLO spaces on RD-spaces and applications to Schrödinger operators
• Morrey and Campanato meet Besov, Lizorkin and Triebel
• Theory of function spaces
• Endpoint properties of localized Riesz transforms and fractional integrals associated to Schrödinger operators
• \(Q\) spaces and Morrey spaces
• Some new tent spaces and duality theorems for fractional Carleson measures and \(Q_{\alpha}(\mathbb R^n)\).
• New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets
• Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers
• Compensated compactness and Hardy spaces
• Multipliers and Morrey spaces
• Local function spaces, heat and Navier-Stokes equations
• A new framework for generalized Besov-type and Triebel–Lizorkin-type spaces
• On the coincidence of certain approaches to smoothness spaces related to Morrey spaces
• The uncertainty principle
• Localized Hardy spaces 𝐻¹ related to admissible functions on RD-spaces and applications to Schrödinger operators
• CONTINUITY OF CALDERÓN–ZYGMUND OPERATORS ON BESOV OR TRIEBEL–LIZORKIN SPACES
• Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrüdinger operators
• Localized Hardy spaces associated with operators
• Q spaces of several real variables
• Atomic decomposition in \(L^p(\mathbb{R}^n)\quad (1<p<\infty)\)