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- W2200204946 abstract "In this paper, we present a local $Tb$ theorem for the non-homogeneous Littlewood-Paley $g_{lambda}^{*}$-function with non-convolution type kernels and upper power bound measure $mu$. We show that, under the assumptions $supp b_Q subset Q$, $|int_Q b_Q dmu| gtrsim mu(Q)$ and $||b_Q||^p_{L^p(mu)} lesssim mu(Q)$, the norm inequality $big| g_{lambda}^{*}(f) big|_{L^p(mu)} lesssim big| f big|_{L^p(mu)}$ holds if and only if the following testing condition holds : $$sup_{Q : cubes in Rn} frac{1}{mu(Q)}int_Q bigg(int_{0}^{ell(Q)} int_{Rn} Big(frac{t}{t+|x-y|}Big)^{mlambda}|theta_t(b_Q)(y,t)|^2 frac{dmu(y) dt}{t^{m+1}}bigg)^{p/2} dmu(x) < infty.$$ This is the first time to investigate $g_lambda^*$-function in the simultaneous presence of three attributes : local, non-homogeneous and $L^p$-testing condition. It is important to note that the testing condition here is $L^p$ type with $p in (1,2]$." @default.
- W2200204946 created "2016-06-24" @default.
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- W2200204946 date "2015-07-19" @default.
- W2200204946 modified "2023-09-27" @default.
- W2200204946 title "A non-homogeneous local $Tb$ theorem for Littlewood-Paley $g_{lambda}^{*}$-function with $L^p$-testing condition" @default.
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