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!
|
| Summary: | 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 . |
|---|---|
| ISSN: | 0972-6802 |