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- W3037904046 abstract "Let $(X,mathscr{B} ,mu )$ be a measure space and ${U_t:-infty <t<infty}$ be a one-parameter ergodic measure preserving flow on $X$. Let $sgeq 2$ and consider the oscillation operator defined as $$mathcal{O}f(x) = left(sum_{k=1}^infty left(max_{substack{n_kleq mleq n_{k+1} min M}}left|A_mf(x)-A_{n_k}f(x)right|right)^sright)^{1/s}$$ where $$A_nf(x) = frac{1}{n}int_0^nf(U_tx), dt$$ is the usual ergodic average. Let $(n_k)$ and $M$ be lacunary sequences then there exist positive constants $C_1$, $C_2$, $C_3$ and $C_p$ such that (a) $|mathcal{O}f|_pleq C_p|f|_p, quad fin L^p(X),quad 1<p<infty,$ (b) $mubig{x:left |mathcal{O}f(x)right |>lambdabig}leq frac{C_1}{lambda}|f|_1,quad fin L^1(X),quadlambda >0,$ (c) $|mathcal{O}f|_1 leq C_2|f|_{H^1},quad fin L^1(X),$ (d) $|mathcal{O}f|_{rm{EBMO}}leq C_3|f|_{infty},quad fin L_c^{infty}(X).$" @default.
- W3037904046 created "2020-07-02" @default.
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- W3037904046 date "2020-06-23" @default.
- W3037904046 modified "2023-09-27" @default.
- W3037904046 title "Inequalities for oscillation operator" @default.
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