Riesz Transform Characterizations for Multidimensional Hardy Spaces

Kania-Strojec, Edyta; Preisner, Marcin

doi:10.1007/s12220-022-00896-1

J Geom Anal

2022

DOI: 10.1007/s12220-022-00896-1

|View full text |Cite

Riesz Transform Characterizations for Multidimensional Hardy Spaces

Edyta Kania-Strojec

Marcin Preisner

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Hardy spaces meet harmonic weights

Preisner¹,

Sikora²,

Yan³

2022

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

We investigate the Hardy space H L 1 H^1_L associated with a self-adjoint operator L L defined in a general setting by Hofmann, Lu, Mitrea, Mitrea, and Yan [Mem. Amer. Math. Soc. 214 (2011), pp. vi+78]. We assume that there exists an L L -harmonic non-negative function h h such that the semigroup exp ⁡ ( − t L ) \exp (-tL) , after applying the Doob transform related to h h , satisfies the upper and lower Gaussian estimates. Under this assumption we describe an illuminating characterisation of the Hardy space H L 1 H^1_L in terms of a simple atomic decomposition associated with the L L -harmonic function h h . Our approach also yields a natural characterisation of the B M O BMO -type space corresponding to the operator L L and dual to H L 1 H^1_L in the same circumstances. The applications include surprisingly wide range of operators, such as: Laplace operators with Dirichlet boundary conditions on some domains in R n {\mathbb {R}^n} , Schrödinger operators with certain potentials, and Bessel operators.

show abstract

Hardy spaces meet harmonic weights

Preisner¹,

Sikora²,

Yan³

2022

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Riesz Transform Characterizations for Multidimensional Hardy Spaces

Cited by 1 publication

References 35 publications

Hardy spaces meet harmonic weights

Hardy spaces meet harmonic weights

Contact Info

Product

Resources

About