Sharp estimates for Schrödinger groups on Hardy spaces for 0 < p ≤ 1

The Anh Bui; Fu Ken Ly

doi:10.1007/s00041-022-09964-0

Sharp estimates for Schrödinger groups on Hardy spaces for 0 < p ≤ 1

The Anh Bui^*, Fu Ken Ly

^*Corresponding author for this work

School of Mathematical and Physical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

23 Downloads (Pure)

Abstract

Let X be a space of homogeneous type with the doubling order n. Let L be a nonnegative self-adjoint operator on L²(X) and suppose that the kernel of e^-^t^L satisfies a Gaussian upper bound. This paper shows that for 0 < p ≤ 1 and s= n(1/p- 1/2) , ‖(I + L)^-se^itLf‖H_L^p(X) ≲ (1+|t|)^s‖f‖H_L^p(X)for all t ∈ R, where H_L^p(X) is the Hardy space associated to L. This recovers the classical results in the particular case when L = - Δ and extends a number of known results.

Original language	English
Article number	70
Pages (from-to)	1-23
Number of pages	23
Journal	Journal of Fourier Analysis and Applications
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s00041-022-09964-0
Publication status	Published - Aug 2022

Bibliographical note

Copyright © 2022, The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Gaussian upper bound
Hardy space
Schrödinger group

Access to Document

10.1007/s00041-022-09964-0Licence: CC BY

Publisher version (open access)Final published version, 541 KBLicence: CC BY

Cite this

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title = "Sharp estimates for Schr{\"o}dinger groups on Hardy spaces for 0 < p ≤ 1",

abstract = "Let X be a space of homogeneous type with the doubling order n. Let L be a nonnegative self-adjoint operator on L2(X) and suppose that the kernel of e-tL satisfies a Gaussian upper bound. This paper shows that for 0 < p ≤ 1 and s= n(1/p- 1/2) , ‖(I + L)-seitLf‖HLp(X) ≲ (1+|t|)s‖f‖HLp(X)for all t ∈ R, where HLp(X) is the Hardy space associated to L. This recovers the classical results in the particular case when L = - Δ and extends a number of known results.",

keywords = "Gaussian upper bound, Hardy space, Schr{\"o}dinger group",

author = "Bui, {The Anh} and Ly, {Fu Ken}",

note = "Copyright {\textcopyright} 2022, The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2022",

month = aug,

doi = "10.1007/s00041-022-09964-0",

language = "English",

volume = "28",

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journal = "Journal of Fourier Analysis and Applications",

issn = "1069-5869",

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TY - JOUR

T1 - Sharp estimates for Schrödinger groups on Hardy spaces for 0 < p ≤ 1

AU - Bui, The Anh

AU - Ly, Fu Ken

N1 - Copyright © 2022, The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2022/8

Y1 - 2022/8

N2 - Let X be a space of homogeneous type with the doubling order n. Let L be a nonnegative self-adjoint operator on L2(X) and suppose that the kernel of e-tL satisfies a Gaussian upper bound. This paper shows that for 0 < p ≤ 1 and s= n(1/p- 1/2) , ‖(I + L)-seitLf‖HLp(X) ≲ (1+|t|)s‖f‖HLp(X)for all t ∈ R, where HLp(X) is the Hardy space associated to L. This recovers the classical results in the particular case when L = - Δ and extends a number of known results.

AB - Let X be a space of homogeneous type with the doubling order n. Let L be a nonnegative self-adjoint operator on L2(X) and suppose that the kernel of e-tL satisfies a Gaussian upper bound. This paper shows that for 0 < p ≤ 1 and s= n(1/p- 1/2) , ‖(I + L)-seitLf‖HLp(X) ≲ (1+|t|)s‖f‖HLp(X)for all t ∈ R, where HLp(X) is the Hardy space associated to L. This recovers the classical results in the particular case when L = - Δ and extends a number of known results.

KW - Gaussian upper bound

KW - Hardy space

KW - Schrödinger group

UR - http://www.scopus.com/inward/record.url?scp=85135844518&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP220100285

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DO - 10.1007/s00041-022-09964-0

M3 - Article

AN - SCOPUS:85135844518

SN - 1069-5869

VL - 28

SP - 1

EP - 23

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 4

M1 - 70

ER -

Sharp estimates for Schrödinger groups on Hardy spaces for 0 < p ≤ 1

Abstract

Bibliographical note

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DP22: Harmonic analysis of Laplacians in curved spaces

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Sharp estimates for Schrödinger groups on Hardy spaces for 0 < p ≤ 1

Abstract

Bibliographical note

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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