Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures
Let µ be a nonnegative Radon measure on ℝd which satisfies the growth condition that there exist constants C0 > 0 and n ∈ (0, d] such that for all x ∈ ℝd and r > 0, μ(B(x,r))≤C0rn, where B(x, r) is the open ball centered at x and having radius r . In this paper, when ℝd is not an initial cube...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/284849 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562631582416896 |
|---|---|
| author | Dachun Yang Dongyong Yang |
| author_facet | Dachun Yang Dongyong Yang |
| author_sort | Dachun Yang |
| collection | DOAJ |
| description | Let µ be a nonnegative Radon measure on ℝd which satisfies the
growth condition that there exist constants C0 > 0 and n ∈ (0, d] such that
for all x ∈ ℝd and r > 0, μ(B(x,r))≤C0rn, where B(x, r) is the open ball
centered at x and having radius r . In this paper, when ℝd is not an initial cube
which implies µ(ℝd) = ∞, the authors prove that the homogeneous Littlewood-Paley g-function of Tolsa is bounded from the Hardy space H1 (µ) to L1(µ), and
furthermore, that if f ∈ RBMO (µ), then [ġ(f )]2 is either infinite everywhere
or finite almost everywhere, and in the latter case, [ġ(f)]2 belongs to RBLO (µ)
with norm no more than C‖f‖RBMO(μ)2, where C≻0 is independent of f . |
| format | Article |
| id | doaj-art-ac76b6b8f0bd4266a83802e46687dfd5 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ac76b6b8f0bd4266a83802e46687dfd52025-02-03T01:22:18ZengWileyJournal of Function Spaces and Applications0972-68022009-01-017218720710.1155/2009/284849Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measuresDachun Yang0Dongyong Yang1School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaLet µ be a nonnegative Radon measure on ℝd which satisfies the growth condition that there exist constants C0 > 0 and n ∈ (0, d] such that for all x ∈ ℝd and r > 0, μ(B(x,r))≤C0rn, where B(x, r) is the open ball centered at x and having radius r . In this paper, when ℝd is not an initial cube which implies µ(ℝd) = ∞, the authors prove that the homogeneous Littlewood-Paley g-function of Tolsa is bounded from the Hardy space H1 (µ) to L1(µ), and furthermore, that if f ∈ RBMO (µ), then [ġ(f )]2 is either infinite everywhere or finite almost everywhere, and in the latter case, [ġ(f)]2 belongs to RBLO (µ) with norm no more than C‖f‖RBMO(μ)2, where C≻0 is independent of f .http://dx.doi.org/10.1155/2009/284849 |
| spellingShingle | Dachun Yang Dongyong Yang Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures Journal of Function Spaces and Applications |
| title | Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures |
| title_full | Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures |
| title_fullStr | Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures |
| title_full_unstemmed | Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures |
| title_short | Endpoint estimates for homogeneous Littlewood-Paley g-functions with non-doubling measures |
| title_sort | endpoint estimates for homogeneous littlewood paley g functions with non doubling measures |
| url | http://dx.doi.org/10.1155/2009/284849 |
| work_keys_str_mv | AT dachunyang endpointestimatesforhomogeneouslittlewoodpaleygfunctionswithnondoublingmeasures AT dongyongyang endpointestimatesforhomogeneouslittlewoodpaleygfunctionswithnondoublingmeasures |