Titlebook: Martingale Spaces and Inequalities; Ruilin Long Book 1993 Springer Fachmedien Wiesbaden 1993 calculus.development.function.nature.variable

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,Φ-inequalities on Martingales,bution” one with slight differences between them. Roughly speaking, by means of the latter, we could get general Φ-inequalities, and by means of the former we lose some generality of Φ, but as a compensation, we get better constants. In this section, we keep the assumptions imposed on (Ω, ., ., {..}

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Book 1993 branch (the key step to accelerate this evolution was D. Burkholder­ R. Gundy-M. Silverstein‘s well-known work in the early 70‘s on the maximal function characterization of Hp), Martingale Hp-BMO Theory soon appeared as a counter­ part of the classical Hp-BMO Theory. Owing to the simplicity of the

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978-3-322-99268-0Springer Fachmedien Wiesbaden 1993

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https://doi.org/10.1007/978-3-322-99266-6calculus; development; function; nature; variable

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,Weight Theory and Weighted Φ-inequalities, which contains .. condition and its extension .. (§6.1–6.2 ), inverse Hülder inequality (§6.3), and the relation between .. weights and . martingales (§6.4–6.5). The last section §6.6 will be devoted to the weighted Φ-inequalities. The assumptions imposed on (Ω, ., ., {..}.) are usual.

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Some Applications of Martingale Techniques in Harmonic Analysis,artingale Theory was one of the sources providing new ideas and methods to the latter. Many good examples showing this could not be put in the book because of the limitation from author’s interests and book’s space. Here we just take two examples to show such significance of Martingale Theory.

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Probabilistic Preliminaries,This chapter will be devoted to the probabilistic preliminaries, such as conditional expectations, stopping times, martingales and its convergences and decompositions, etc., which are needed in what follows. It is probably useful for those who are not familiar with Probability Theory.

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