NDLI: Hardy spaces H $^{ p }$ over non-homogeneous metric measure spaces and their applications

Please wait, while we are loading the content...

Science in China Series A: Mathematics : Volume 60

Science in China Series A: Mathematics : Volume 59

Science in China Series A: Mathematics : Volume 58

Science in China Series A: Mathematics : Volume 58, Issue 12, December 2015

Science in China Series A: Mathematics : Volume 58, Issue 11, November 2015

Science in China Series A: Mathematics : Volume 58, Issue 10, October 2015

Science in China Series A: Mathematics : Volume 58, Issue 9, September 2015

Science in China Series A: Mathematics : Volume 58, Issue 8, August 2015

Science in China Series A: Mathematics : Volume 58, Issue 7, July 2015

Science in China Series A: Mathematics : Volume 58, Issue 6, June 2015

Science in China Series A: Mathematics : Volume 58, Issue 5, May 2015

Science in China Series A: Mathematics : Volume 58, Issue 4, April 2015

Science in China Series A: Mathematics : Volume 58, Issue 3, March 2015

Science in China Series A: Mathematics : Volume 58, Issue 2, February 2015

Objective triangle functors

Multiplicity one theorems, S-version

Ground states of a nonlinear Schrödinger system with nonconstant potentials

Integrable discretization of soliton equations via bilinear method and Bäcklund transformation

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

Hardy spaces H $^{ p }$ over non-homogeneous metric measure spaces and their applications

A Marcinkiewicz criterion for L $^{ p }$-multipliers related to Schrödinger operators with constant magnetic fields

Weakly k-hyponormal and polynomially hyponormal commuting operator pairs

A Cheeger-Müller theorem for symmetric bilinear torsions on manifolds with boundary

Gradient estimates and coupling property for semilinear SDEs driven by jump processes

Science in China Series A: Mathematics : Volume 58, Issue 1, January 2015

Science in China Series A: Mathematics : Volume 57

Science in China Series A: Mathematics : Volume 56

Science in China Series A: Mathematics : Volume 55

Science in China Series A: Mathematics : Volume 54

Science in China Series A: Mathematics : Volume 53

Science in China Series A: Mathematics : Volume 52

Science in China Series A: Mathematics : Volume 51

Science in China Series A: Mathematics : Volume 50

Science in China Series A: Mathematics : Volume 49

Science in China Series A: Mathematics : Volume 48

Science in China Series A: Mathematics : Volume 47

Science in China Series A: Mathematics : Volume 46

Science in China Series A: Mathematics : Volume 45

Science in China Series A: Mathematics : Volume 44

Science in China Series A: Mathematics : Volume 43

Science in China Series A: Mathematics : Volume 42

Science in China Series A: Mathematics : Volume 41

Science in China Series A: Mathematics : Volume 40

Hardy spaces H $^{ p }$ over non-homogeneous metric measure spaces and their applications

Content Provider	Springer Nature Link
Author	Fu, Xing Lin, HaiBo Yang, DaChun Yang, DongYong
Copyright Year	2015
Abstract	Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Let ρ ∈ (1, ∞), 0 < p ⩽ 1 ⩽ q ⩽ ∞, p ≠ q, γ ∈ [1, ∞) and ε ∈ (0, ∞). In this paper, the authors introduce the atomic Hardy space $$\tilde H_{atb,\rho }^{p,q,\gamma } (\mu )$$ and the molecular Hardy space $$\tilde H_{mb,\rho }^{p,q,\gamma ,\varepsilon } (\mu )$$ via the discrete coefficient $$\tilde K_{B,S}^{(\rho ),p}$$ , and prove that the Calderón-Zygmund operator is bounded from $$\tilde H_{mb,\rho }^{p,q,\gamma ,\delta } (\mu )$$ (or $$\tilde H_{atb,\rho }^{p,q,\gamma } (\mu )$$ ) into L $^{ p }$(μ), and from $$\tilde H_{atb,\rho (\rho + 1)}^{p,q,\gamma + 1} (\mu )$$ into $$\tilde H_{mb,\rho }^{p,q,\gamma ,\tfrac{1} {2}(\delta - \tfrac{v} {p} + v)} (\mu )$$ . The boundedness of the generalized fractional integral T $_{ β }$ (β ∈ (0, 1)) from $$\tilde H_{mb,\rho }^{p_1 ,q,\gamma ,\theta } (\mu )$$ (or $$\tilde H_{atb,\rho }^{p_1 ,q,\gamma } (\mu )$$ ) into $$L^{p_2 } (\mu )$$ with 1/p $_{2}$ = 1/p $_{1}$−β is also established. The authors also introduce the ρ-weakly doubling condition, with ρ ∈ (1, ∞), of the measure μ and construct a non-doubling measure μ satisfying this condition. If μ is ρ-weakly doubling, the authors further introduce the Campanato space $$\mathcal{E}_{\rho ,\eta ,\gamma }^{\alpha ,q} (\mu )$$ and show that $$\mathcal{E}_{\rho ,\eta ,\gamma }^{\alpha ,q} (\mu )$$ is independent of the choices of ρ, η, γ and q; the authors then introduce the atomic Hardy space $$\hat H_{atb,\rho }^{p,q,\gamma } (\mu )$$ and the molecular Hardy space $$\hat H_{mb,\rho }^{p,q,\gamma ,\varepsilon } (\mu )$$ , which coincide with each other; the authors finally prove that $$\hat H_{atb,\rho }^{p,q,\gamma } (\mu )$$ is the predual of $$\mathcal{E}_{\rho ,\rho ,1}^{1/p - 1,1} (\mu )$$ . Moreover, if μ is doubling, the authors show that $$\mathcal{E}_{\rho ,\eta ,\gamma }^{\alpha ,q} (\mu )$$ and the Lipschitz space Lip$_{ α, q }$(μ) (q ∈ [1, ∞)), or $$\hat H_{atb,\rho }^{p,q,\gamma } (\mu )$$ and the atomic Hardy space H at p, q (μ) (q ∈ (1, ∞]) of Coifman and Weiss coincide. Finally, if (X, d, μ) is an RD-spac (reverse doubling space) with μ(X) = ∞, the authors prove that $$\tilde H_{atb,\rho }^{p,q,\gamma } (\mu )$$ , $$\tilde H_{mb,\rho }^{p,q,\gamma ,\varepsilon } (\mu )$$ and H at p, q (μ) coincide for any q ∈ (1, 2]. In particular, when (X, d, μ):= (ℝ$^{ D }$, \|·\|, dx) with dx being the D-dimensional Lebesgue measure, the authors show that spaces $$\tilde H_{atb,\rho }^{p,q,\gamma } (\mu )$$ , $$\tilde H_{mb,\rho }^{p,q,\gamma ,\varepsilon } (\mu )$$ , $$\hat H_{atb,\rho }^{p,q,\gamma } (\mu )$$ and $$\hat H_{mb,\rho }^{p,q,\gamma ,\varepsilon } (\mu )$$ all coincide with H $^{ p }$(ℝ$^{ D }$) for any q ∈ (1, ∞).
Starting Page	309
Ending Page	388
Page Count	80
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	58
Issue Number	2
e-ISSN	18691862
Language	English
Publisher	Science China Press
Publisher Date	2015-01-07
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	non-homogeneous metric measure space ρ-weakly doubling measure Hardy space Campanato space Lipschitz space Calderón-Zygmund operator atomic block molecular block Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Boundedness of Calderón-Zygmund operators with finite non-doubling measures

Hardy spaces $H^p$ over non-homogeneous metric measure spaces and their applications

A Remark on the Boundedness of Calderón–Zygmund Operators in Nony–homogeneous Spaces

Multilinear Calderón-Zygmund operator on products of Hardy spaces

Atomic hardy-type spaces between H 1 and L 1 on metric spaces with non-doubling measures

Boundedness of linear operators via atoms on hardy spaces with non-doubling measures (2009).

Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures, Publ

Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures, Publ

Θ-type Calderón-Zygmund operators with non-doubling measures

Hardy spaces H $^{ p }$ over non-homogeneous metric measure spaces and their applications

Similar Documents

Boundedness of Calderón-Zygmund operators with finite non-doubling measures

Hardy spaces $H^p$ over non-homogeneous metric measure spaces and their applications

A Remark on the Boundedness of Calderón–Zygmund Operators in Nony–homogeneous Spaces

Multilinear Calderón-Zygmund operator on products of Hardy spaces

Atomic hardy-type spaces between H 1 and L 1 on metric spaces with non-doubling measures

Boundedness of linear operators via atoms on hardy spaces with non-doubling measures (2009).

Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures, Publ

Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures, Publ

Θ-type Calderón-Zygmund operators with non-doubling measures

Hardy spaces H $^{ p }$ over non-homogeneous metric measure spaces and their applications