Weak-type endpoint bounds for Riesz means

Terence Tao

Type: Article

Publication Date: 1996-01-01

Citations: 26

DOI: https://doi.org/10.1090/s0002-9939-96-03371-0

Abstract

We use <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> restriction theory to prove optimal weak-type bounds of Bochner-Riesz multipliers and Riesz means of elliptic pseudo-differential operators on compact manifolds, for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p less-than-or-equal-to 2 left-parenthesis n plus 1 right-parenthesis slash left-parenthesis n plus 3 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">p \leq 2(n+1)/(n+3)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Locations

Proceedings of the American Mathematical Society - View - PDF
Proceedings of the American Mathematical Society - View - PDF
Proceedings of the American Mathematical Society - View - PDF

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