Abstract
An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12326307
Award Identifier / Grant number: 12326308
Award Identifier / Grant number: 12271483
Funding source: Natural Science Foundation of Zhejiang Province
Award Identifier / Grant number: LQ17A010002
Funding statement: This research was funded by National Natural Science Foundation of China (grant numbers 12326307, 12326308, 12271483) and Natural Science Foundation of Zhejiang Province (grant number LQ17A010002).
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Communicated by: Christopher D. Sogge
References
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Articles in the same Issue
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- Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
- Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
- Estimates of Picard modular cusp forms
- Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
- Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
- Free groups generated by two unipotent maps
- Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
- Colored multizeta values in positive characteristic
- Simultaneous nonvanishing of central L-values with large level
- Laplace convolutions of weighted averages of arithmetical functions
- Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
- On the geometric trace of a generalized Selberg trace formula
- Elementary properties of free lattices
- Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
- Small generators of abelian number fields
- Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
- Weighted bilinear multiplier theorems in Dunkl setting via singular integrals
Articles in the same Issue
- Frontmatter
- Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
- Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
- Estimates of Picard modular cusp forms
- Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
- Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
- Free groups generated by two unipotent maps
- Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
- Colored multizeta values in positive characteristic
- Simultaneous nonvanishing of central L-values with large level
- Laplace convolutions of weighted averages of arithmetical functions
- Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
- On the geometric trace of a generalized Selberg trace formula
- Elementary properties of free lattices
- Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
- Small generators of abelian number fields
- Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
- Weighted bilinear multiplier theorems in Dunkl setting via singular integrals