The Linear Bound for the Natural Weighted Resolution of the Haar Shift

الأصل · EN

The Hilbert transform has a linear bound in the A₂ characteristic on weighted L², equation* H ₗ²₍w₎→ ₗ²₍w₎ [w] ₐ₂, equation* and we extend this linear bound to the nine constituent operators in the natural weighted resolution of the conjugation Mw¹/²S Mw⁻¹/² induced by the canonical decomposition of a multiplier into paraproducts:% equation* Mf=Pf⁻+Pf⁰+Pf⁺. equation* The main tools used are composition of paraproducts, a product formula for Haar coefficients, the Carleson Embedding Theorem, and the linear bound for the square function.