Sharp general local estimates for dyadic-like maximal operators and related Bellman functions (Q960570)

Let \(G,H\) be two increasing and convex functions mapping \([0,+\infty)\) into itself and such that \(\limsup_{x\to+\infty} G(x)/H(x)>0\). Let \(T\) be a tree, i.e. a set of measurable subsets of \(X\) satisfying suitable conditions. There are obtained evaluations and estimations of the Bellman function \(G^T_{G,H}(F,f,L,k)\) in a number of important cases, including \(G(x)=x^p/p\), \(H(x)=x^q\) with \(1\leq q<p\).