The John-Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the sharp maximal function of Fefferman-Stein, while the second one concerns local weighted mean oscillations, generalizing a result of Muckenhoupt and Wheeden. Applications to the context of generalized Poincaré type inequalities and to the context of the Cp class of weights are given. Extensions to the case of polynomial BMO type spaces are also given.
We prove an appropriate sharp quantitative reverse Hölder inequality for the C p class of weights from which we obtain as a limiting case the sharp reverse Hölder inequality for the A ∞ class of weights [13, 14]. We use this result to provide a quantitative weighted norm inequality between Calderón-Zygmund operators and the Hardy-Littlewood maximal function, precisely T f L p (w) T,n,p,q [w] Cq (1 + log + [w] Cq) M f L p (w) , for w ∈ C q and q > p > 1, quantifying Sawyer's theorem [26].
This paper presents a discussion of our "yguazti-a" code, which integrates systems of differential equations (generally, the gasdynamic or MHD equations together with an atomic/chemical network) on a hierarchical binary adaptive grid. Examples of recent calculations are shown, and a general discussion of the capabilities of the code and the published results is presented,
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