English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting,and under the assumption of dual exponents. This Theorem provides a flexibleframework for proving the boundedness of a Calder\'on-Zygmund operator,supposing the existence of systems of local accretive functions. We assume thatthe integrability exponents on these systems of functions are of the form$1/p+1/q\le 1$, and provide a direct proof. The principal point of interest isin the use of random grids and the corresponding construction of the corona. Wealso utilize certain twisted martingale transform inequalities.

On the Local $Tb$ Theorem: A Direct Proof under Duality Assumption