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Refined Strichartz inequalities for the wave equation

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Terence L. J. Harris

Analysis of PDEs · Submitted 18 May 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$.

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arXiv ID1805.07146 (version 5)
Pith IDY6MYRLPK, Pith's permanent record of this paper and its review
CitationTerence L. J. Harris. "Refined Strichartz inequalities for the wave equation." arXiv:1805.07146 (2018). https://pith.science/paper/Y6MYRLPK
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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.85 · mentions code or data availability 0.02.

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arXiv listing abstract v5. Results and the main claim are underlined; .

Some analogues of the Schr\"odinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Some analogues of the Schr\"odinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. contribution 0.71 0.92 0.51 asserted 1.00
s1 These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$. result 0.74 0.87 0.44 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Some analogues of the Schr\"odinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in dimensions $d \geq 4$.

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References
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3 arXiv papers cite this in 8 sentences

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Papers citing it · 6 sentences without a confident label

Compares with it 1 paper
  • The main result of this work is the lower bound [equation] This is probably not sharp for $d ≥4$, but it supersedes the lower bound from [ref] (the exact value $β(α, Γ^d ) = α-1$ for $α∈[d,d+1]$ is known in every dimension [ref] ).

    Improved decay of conical averages of the Fourier transform · Introduction · 0.99

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What it cites · 18 sentences without a confident label

Uses the method or tool of 2 papers
Cites as background 3 papers
  • For $q ∈[1,∞]$, let $s_d(α,q)$ be the infimum over all $s$ satisfying the inequality [equation] where [equation] and [equation] The quantity $s_d(α,2)$ is related to $β(α,Γ^d)$ through the equation [equation] see [ref] ; a proof is given here in Proposition [ref].

    Falconer's distance set problem via the wave equation · Introduction · 0.86

  • The distance set problem is related to the case where $Γ= S^n-1$ [ref] , see also [ref] for the connection between $β(α, S^n-1)$ and the pointwise convergence of solutions to the wave and Schrödinger equations.

    Average decay of the Fourier transform of measures with applications · Introduction · 0.92

  • The distance set problem is related to the case where $Γ= S^n-1$ [ref] , see also [ref] for the connection between $β(α, S^n-1)$ and the pointwise convergence of solutions to the wave and Schrödinger equations.

    An $L^2$-identity and pinned distance problem · Introduction · 0.92

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