Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups

DOI10.1016/j.matpur.2018.06.012zbMath1415.43002arXiv1803.01153OpenAlexW2962875380WikidataQ115343520 ScholiaQ115343520MaRDI QIDQ1732998

Brett D. Wick, Hong-Quan Li, Xuan Thinh Duong, Ji Li

Publication date: 26 March 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01153

zbMATH Keywords

Riesz transformsBMO spacecommutatordiv-curl lemmastratified nilpotent Lie groups

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Analysis on other specific Lie groups (43A80) Analysis on ordered groups, (H^p)-theory (43A17)

Related Items

Two weight commutators on spaces of homogeneous type and applications ⋮ A new vanishing Lipschitz-type subspace of BMO and compactness of bilinear commutators ⋮ Commutators, BMO, Hardy spaces and factorization: a survey ⋮ Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups ⋮ John-Nirenberg-\(Q\) spaces via congruent cubes ⋮ Nontriviality of John-Nirenberg-Campanato spaces ⋮ The $L^p$-to-$L^q$ compactness of commutators with $p \gt q$ ⋮ Schatten classes and commutators of Riesz transform on Heisenberg group and applications ⋮ The \(L^p\)-to-\(L^q\) boundedness of commutators with applications to the Jacobian operator ⋮ Unnamed Item ⋮ Commutators on weighted Morrey spaces on spaces of homogeneous type ⋮ Commutators of Cauchy-Szego type integrals for domains in C^n with minimal smoothness ⋮ Compactness of Riesz transform commutator on stratified Lie groups ⋮ The commutators of Bochner-Riesz operators for elliptic operators

Cites Work

• Unnamed Item
• Unnamed Item
• Commutators in the two-weight setting
• Characterizations of \(H_{\Delta_N}^1(\mathbb{R}^n)\) and \(\operatorname{BMO}_{\Delta_N}(\mathbb{R}^n)\) via weak factorizations and commutators
• On bounded bilinear forms
• Singular integral characterizations of Hardy spaces on homogeneous groups
• The factorization of \(H^p\) on the space of homogeneous type
• Factorization theorems for Hardy spaces in several variables
• Product BMO, little BMO, and Riesz commutators in the Bessel setting
• Compensated compactness and Hardy spaces
• Two weight commutators in the Dirichlet and Neumann Laplacian settings
• Nonhomogeneous div-curl lemmas and local Hardy spaces
• The unified theory for the necessity of bounded commutators and applications
• Classical Fourier Analysis
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Commutators of singular integrals revisited
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• The Cauchy integral, bounded and compact commutators
• Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting
• DIV–CURL TYPE THEOREM, H-CONVERGENCE AND STOKES FORMULA IN THE HEISENBERG GROUP