𝑇1 theorems for Besov and Triebel-Lizorkin spaces

Abstract

We give simple proofs of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Baseline 1"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">T1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> theorem in the general context of Besov spaces and (weighted) Triebel-Lizorkin spaces. Our approach yields some new results for kernels satisfying weakened regularity conditions, while also recovering previously known results.

Locations

• Transactions of the American Mathematical Society - View - PDF