A convolution estimate for a measure on a curve in $\mathbb {R}^4$

DOI10.1090/S0002-9939-97-03716-7zbMath0972.42006MaRDI QIDQ4336591

Daniel M. Oberlin

Publication date: 13 May 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

measures\(L^p\)-estimatesconvolution operator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Multipliers for harmonic analysis in several variables (42B15)

Related Items (11)

Decay estimates for oscillatory integrals with polynomial phase. ⋮ Decay estimates for oscillatory integrals with polynomial phase in terms of \(p^{(n-3)}\) and \(p^{(n-2)}\) or in terms of \(p^{(n-2)}\) and \(p^{(n-1)}\) ⋮ 𝐿^{𝑝} improving bounds for averages along curves ⋮ Endpoint \(L^p \rightarrow L^q\) bounds for integration along certain polynomial curves ⋮ Convolution estimates for measures on some complex curves ⋮ Uniform \(L_x^p - L_{x, r}^q\) improving for dilated averages over polynomial curves ⋮ Uniform sublevel Radon-like inequalities ⋮ \(L^p\) improving multilinear Radon-like transforms ⋮ Metrics and smoothing of translation-invariant Radon transforms along curves. ⋮ Capacity and potentials on curves ⋮ Generalized curvature for certain Radon-like operators of intermediate dimension

Cites Work

• Unnamed Item
• A convolution inequality concerning Cantor-Lebesgue measures
• $L^p$-Improving Properties for Some Measures Supported on Curves.
• Degenerate curves and harmonic analysis
• Oscillatory integrals with polynomial phase.
• A Remark on Convolution With Measures Supported on Curves
• Convolution estimates for some degenerate curves
• Damping oscillatory integrals with polynomial phase.
• Convolution Estimates for Some Measures on Curves

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