2 results
A WEIGHTED
$\boldsymbol {L}^{\boldsymbol {2}}$ ESTIMATE OF COMMUTATORS OF BOCHNER–RIESZ OPERATORS FOR HERMITE OPERATOR
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 116 / Issue 3 / June 2024
- Published online by Cambridge University Press:
- 15 January 2024, pp. 308-330
- Print publication:
- June 2024
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Let H be the Hermite operator
$-\Delta +|x|^2$ on 
$\mathbb {R}^n$. We prove a weighted 
$L^2$ estimate of the maximal commutator operator 
$\sup _{R>0}|[b, S_R^\lambda (H)](f)|$, where 
$ [b, S_R^\lambda (H)](f) = bS_R^\lambda (H) f - S_R^\lambda (H)(bf) $ is the commutator of a BMO function b and the Bochner–Riesz means 
$S_R^\lambda (H)$ for the Hermite operator H. As an application, we obtain the almost everywhere convergence of 
$[b, S_R^\lambda (H)](f)$ for large 
$\lambda $ and 
$f\in L^p(\mathbb {R}^n)$.
Weighted estimates for Bochner–Riesz operators on Lorentz spaces
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 2 / April 2023
- Published online by Cambridge University Press:
- 28 February 2022, pp. 654-678
- Print publication:
- April 2023
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We present new estimates in the setting of weighted Lorentz spaces of operators satisfying a limited Rubio de Francia condition; namely $T$
is bounded on $L^{p}(v)$
for every $v$
in an strictly smaller class of weights than the Muckenhoupt class $A_p$
. Important examples will be the Bochner–Riesz operators $BR_\lambda$
with $0<\lambda <{(n-1)}/2$
, sparse operators, Hörmander multipliers with a limited regularity condition and rough operators with $\Omega \in L^{r}(\Sigma )$
, $1 < r < \infty$
.
