广义Calderón-Zygmund算子的一个权模不等式

WEIGHTED NORM INEQUALITIES FOR GENERALIZED CALDERO'NZYGMUND OPERATORS

本文证明了如下的广义Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子的一个权模不等式∫Ｒｎ｜Ｔｆ（ｘ）｜ｐｗ（ｘ）ｄｘ≤Ｃ∫Ｒｎ｜ｆ（ｘ）｜ｐＭ［ｐ］＋１ｗ（ｘ）ｄｘ其中Ｔ是θ（ｔ）型Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子，Ｍｋ是取ｋ次Ｈａｒｄｙ－Ｌｉｔｌｅｗｏｏｄ极大算子，［ｐ］是ｐ的整数部分，１＜ｐ＜＋∞．

In this paper, we show that the following weighted norm inequalities of generalized CalderónZygmund operators holds∫Rn|Tf(x)|pw(x)dx≤C∫Rn|f(x)|pM+1w(x)dxwhere T is a θ(t) type CalderónZygmund operator, Mk is the HardyLittlewood maximal operator M iterated k times, and  is the integer part of p, 1<p<+∞. We also give the following resultw({x∈Rn∶|Tf(x)|>λ})≤Cλ ∫Rn|f(x)|M2w(x)dx