Abstract
We show that if a pair of weights (u, ) satisfies a sharp Ap - bump condition in the scale of all log bumps certain loglog bumps , then Haar shifts map
( ) into
(u) with a constant quadratic in the complexity of the shift . This in turn implies the two weight boundedness for all Calderón – Zygmund operators. We obtain a generalized version of the former theorem valid for a larger family of Calderón – Zygmund operators in any ambient space . We present a bilinear Tb theorem for singular operators Calderón – Zygmund type. Extending the end point results obtained to maximal singular. Another consequence is a quantitative two weight bump estimate.
Ibrahim, H (2021). Logarithmic Bump With Bilinear T (B) Theorem And Maximal Singular Integral Operators. Afribary. Retrieved from https://afribary.com/works/logarithmic-bump-with-bilinear-t-b-theorem-and-maximal-singular-integral-operators
Ibrahim, Hind "Logarithmic Bump With Bilinear T (B) Theorem And Maximal Singular Integral Operators" Afribary. Afribary, 21 May. 2021, https://afribary.com/works/logarithmic-bump-with-bilinear-t-b-theorem-and-maximal-singular-integral-operators. Accessed 02 May. 2024.
Ibrahim, Hind . "Logarithmic Bump With Bilinear T (B) Theorem And Maximal Singular Integral Operators". Afribary, Afribary, 21 May. 2021. Web. 02 May. 2024. < https://afribary.com/works/logarithmic-bump-with-bilinear-t-b-theorem-and-maximal-singular-integral-operators >.
Ibrahim, Hind . "Logarithmic Bump With Bilinear T (B) Theorem And Maximal Singular Integral Operators" Afribary (2021). Accessed May 02, 2024. https://afribary.com/works/logarithmic-bump-with-bilinear-t-b-theorem-and-maximal-singular-integral-operators