# Two problems associated with convex finite type domains.

Alexander Iosevich; Eric Sawyer; Andreas Seeger

Publicacions Matemàtiques (2002)

- Volume: 46, Issue: 1, page 153-177
- ISSN: 0214-1493

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topIosevich, Alexander, Sawyer, Eric, and Seeger, Andreas. "Two problems associated with convex finite type domains.." Publicacions Matemàtiques 46.1 (2002): 153-177. <http://eudml.org/doc/41448>.

@article{Iosevich2002,

abstract = {We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp Lp estimates for p > 4, generalizing the Carleson-Sjölin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.},

author = {Iosevich, Alexander, Sawyer, Eric, Seeger, Andreas},

journal = {Publicacions Matemàtiques},

keywords = {Análisis de Fourier; Medias de Riesz; Dominios convexos; Hipersuperficies; quasiradial Bochner-Riesz means; lattice points; convex bodies; finite line type; Carleson-Sjölin theorem},

language = {eng},

number = {1},

pages = {153-177},

title = {Two problems associated with convex finite type domains.},

url = {http://eudml.org/doc/41448},

volume = {46},

year = {2002},

}

TY - JOUR

AU - Iosevich, Alexander

AU - Sawyer, Eric

AU - Seeger, Andreas

TI - Two problems associated with convex finite type domains.

JO - Publicacions Matemàtiques

PY - 2002

VL - 46

IS - 1

SP - 153

EP - 177

AB - We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp Lp estimates for p > 4, generalizing the Carleson-Sjölin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.

LA - eng

KW - Análisis de Fourier; Medias de Riesz; Dominios convexos; Hipersuperficies; quasiradial Bochner-Riesz means; lattice points; convex bodies; finite line type; Carleson-Sjölin theorem

UR - http://eudml.org/doc/41448

ER -

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