The Lp-Lp mapping properties of convolution operators with the affine arclength measure on space curves

DOI10.1017/S144678870000375XzbMath1037.42012MaRDI QIDQ4458284

Youngwoo Choi

Publication date: 17 March 2004

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

zbMATH Keywords

affine arclength measureflat curve

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Multipliers for harmonic analysis in several variables (42B15)

Related Items (6)

Universal \(L^p\) improving for averages along polynomial curves in low dimensions ⋮ Convolution estimates related to space curves ⋮ Endpoint \(L^p \rightarrow L^q\) bounds for integration along certain polynomial curves ⋮ Convolution estimates for measures on some complex curves ⋮ Convolution with measures on flat curves in low dimensions ⋮ Generalized curvature for certain Radon-like operators of intermediate dimension

Cites Work

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• Harmonic analysis on nilpotent groups and singular integrals. III: Fractional integration along manifolds
• $L^p$-Improving Properties for Some Measures Supported on Curves.
• Degenerate curves and harmonic analysis
• A Remark on Convolution With Measures Supported on Curves
• Convolution estimates for some degenerate curves
• Fractional integration along homogeneous curves in $R^3$
• Convolution Estimates for Some Measures on Curves
• 𝐿^{𝑝} improving bounds for averages along curves

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