A note on failure of energy reversal for classical fractional singular integrals

Abstract

For alpha in [0,n) we demonstrate the failure of energy reversal for the vector of alpha-fractional Riesz transforms, and more generally for any vector of alpha-fractional convolution singular integrals having a kernel with vanishing integral on every great circle of the sphere.

24 pages. This version references a correct form of the T1 theorem, corrects typos and uses Bochner's theorem to complete the proof for the missing range of alpha, and also points out an easy extension to higher dimensions. arXiv admin note: text overlap with arXiv:1305.5104

References in corpus (2)

• Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension Weights
• A geometric condition, necessity of energy, and two weight boundedness of fractional Riesz transforms

Cited by in corpus (1)

• A geometric condition, necessity of energy, and two weight boundedness of fractional Riesz transforms