Improved Cotlar's inequality in the context of local <em>Tb</em> theorems

In the context of local theorems with testing conditions we prove an enhanced Cotlar's inequality. This is related to the problem of removing the so called buffer assumption of Hytönen–Nazarov, which is the final barrier for the full solution of S. Hofmann's problem. We also investigate the problem of extending the Hytönen–Nazarov result to non-homogeneous measures. We work not just with the Lebesgue measure but with measures in satisfying , . The range of exponents in the Cotlar type inequality depend on . Without assuming buffer we get the full range of exponents for measures with , and in general we get , . Consequences for (non-homogeneous) local theorems are discussed.

在带有检验条件的局部定理的背景下，我们证明了一个强化的科特拉尔（Cotlar）不等式。这与去除海托宁 - 纳扎罗夫（Hytönen - Nazarov）所谓的缓冲假设的问题有关，该假设是完全解决S. 霍夫曼（S. Hofmann）问题的最终障碍。我们还研究了将海托宁 - 纳扎罗夫的结果推广到非齐次测度的问题。我们不仅处理勒贝格测度，还处理满足[此处应有相关条件缺失]的测度。科特拉尔型不等式中指数的范围取决于[此处应有相关内容缺失]。在不假设缓冲的情况下，对于满足[此处应有相关条件缺失]的测度，我们得到指数的完整范围，并且一般来说我们得到[此处应有相关内容缺失]。讨论了（非齐次）局部定理的结果。