Weighted inequalities for some spherical maximal operators

Duoandikoetxea, Javier; Seijo, Edurne

doi:10.1215/ijm/1258138481

Cited by 3 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results in [Var94,MS95,Tan01] are in this direction for the case of Kakeya. For the spherical maximal function, we refer the reader to [DV96] and [DS02] for several results concerning power weights of the form w(x) = |x| α . Here, as in the case of Kakeya, there is no geometric A p condition as in the case of HL maximal function.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weighted Estimates for Maximal Functions Associated to Skeletons

Olivo

Rela

2019

J Geom Anal

View full text Add to dashboard Cite

We provide quantitative weighted estimates for the L p (w) norm of a maximal operator associated to cube skeletons in R n . The method of proof differs from the usual in the area of weighted inequalities since there are no covering arguments suitable for the geometry of skeletons. We use instead a combinatorial strategy that allows to obtain, after a linearization and discretization, L p bounds for the maximal operator from an estimate related to intersections between skeletons and k-planes.1991 Mathematics Subject Classification. Primary: 42B25. Secondary: 43A85.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weighted Estimates for Maximal Functions Associated to Skeletons

Olivo

Rela

2019

J Geom Anal

View full text Add to dashboard Cite

show abstract

“…for 1 − n < α < n(p − 1) − p and (1.9) does not hold for α < 1 − n. While for general M E this was considered in [19].…”

Section: Spherical Meansmentioning

confidence: 99%

Estimates at or beyond endpoint in harmonic analysis: Bochner-Riesz means and spherical means

Long

2011

Preprint

View full text Add to dashboard Cite

We introduce some new functions spaces to investigate some problems at or beyond endpoint. First, we prove that Bochner-Riesz means B λ R are bounded from some subspaces of), and 0 < R < ∞, and so are the maximal Bochner-Riesz means B λ *. From these we obtain the L p |x| α -norm convergent property of B λ R for these λ, p, and α. Second, let n ≥ 3, we prove that the maximal spherical means are bounded from some subspaces of L p |x| α to L p |x| α for 0 < p ≤ n n−1 and −n(1− p 2 ) < α < n(p−1)−n. We also obtain a L p |x| α -norm convergent property of the spherical means for such p and α. Finally, we prove that some new types of |x| α -weighted estimates hold at or beyond endpoint for many operators, such as Hardy-Littlewood maximal operator, some maximal and truncated singular integral operators, the maximal Carleson operator, etc. The new estimates can be regarded as some substitutes for the (H p , H p ) and (H p , L p ) estimates for the operators which fail to be of types (H p , H p ) and (H p , L p ).

show abstract

Multi-Parameter Maximal Operators Associated with Finite Measures and Arbitrary Sets of Parameters

Heo

2016

Integr. Equ. Oper. Theory

View full text Add to dashboard Cite

Weighted inequalities for some spherical maximal operators

Cited by 3 publications

References 6 publications

Weighted Estimates for Maximal Functions Associated to Skeletons

Weighted Estimates for Maximal Functions Associated to Skeletons

Estimates at or beyond endpoint in harmonic analysis: Bochner-Riesz means and spherical means

Multi-Parameter Maximal Operators Associated with Finite Measures and Arbitrary Sets of Parameters

Contact Info

Product

Resources

About