科研之友
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摘要
Suppose that f is a martingale and let |f|*, S(f) denote the associated maximal and square functions. We prove that for any weight omega we have parallel to |f|* parallel to(L1)(omega) <= C parallel to S(f)parallel to(L1)(omega*) with C = 16(root 2+1) = 38.62742....The proof rests on the construction of an appropriate special function, enjoying certain size and concavity conditions. Furthermore, we show that the term omega* on the right cannot be replaced by the r-maximal function of omega for any 0 < r < 1.
- 出版日期2017-10
