Fractal Strichartz estimate for the wave equation

Cho, Chu-Hee; Ham, Seheon; Lee, Sanghyuk

doi:10.1016/j.na.2016.11.006

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction4

Product Sets1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2024

Publication Types

Select...

Article6

Other2

Relationship

Self Cite3

Independent5

Authors

Journals

Cited by 15 publications

(29 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…I am not aware of such results. However, in addition to the spherical averages (discussed in Section 4), which have been studied for a long time, there are recent estimates for cones and hyperboloids; see [2], [13], and [1].…”

Section: Product Setsmentioning

confidence: 99%

Hausdorff dimension and projections related to intersections

Mattila¹

2022

Publicacions Matemàtiques

View full text Add to dashboard Cite

show abstract

Section: Product Setsmentioning

confidence: 99%

Hausdorff dimension and projections related to intersections

Mattila¹

2022

Publicacions Matemàtiques

View full text Add to dashboard Cite

show abstract

“…In this paper we take an alternative approach which relies on the fractal Strichartz estimate with respect to a measure (see (1.7) below), which was previously studied by some authors (see [22,7,2,10,18]). Via the approach we prove the conjecture (1.2) when d = 3 and improve the previously known results (see (1.4)) for higher dimensions d ≥ 4 and…”

Section: Introductionmentioning

confidence: 99%

Dimension of divergence set of the wave equation

Ham¹,

Ko²,

Lee³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider the Hausdorff dimension of the divergence set on which the pointwise convergence lim t→0 e itWe especially prove the conjecture raised by Barceló, Bennett, Carbery and Rogers [1] for d = 3, and improve the previous results in higher dimensions d ≥ 4. We also show that a Strichartz type estimate for f → e it √ −∆ f with the measure dt dµ(x) is essentially equivalent to the estimate for the spherical average of µ which has been extensively studied for the Falconer distance set problem. The equivalence provides shortcuts to the recent results due to Liu [11] and Rogers [18].

show abstract

“…When d ≥ 3 the estimate (1.4) is relatively easier to obtain. There are various estimates which are straightforward consequences of the fractal Strichartz estimates for the wave equation ( [8,13]). We discuss the matter in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Circular average relative to fractal measures

Ham,

Ko,

Lee

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We prove new L p -L q estimates for averages over dilates of the circle with respect to α-dimensional fractal measure, which unify different types of maximal estimates for the circular average. Our results are consequences of L p -L q smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages. 2020 Mathematics Subject Classification. 42B25. Key words and phrases. circular average, general measures.

show abstract

Fractal Strichartz estimate for the wave equation

Abstract: Abstract. We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions. In R 3+1 we obtain the sharp estimate and in higher dimensions improve the previous results.

Cited by 15 publications

References 30 publications

Hausdorff dimension and projections related to intersections

Hausdorff dimension and projections related to intersections

Dimension of divergence set of the wave equation

Circular average relative to fractal measures

Contact Info

Product

Resources

About