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This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
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V. 12 contains: The Archer...Christmas, 1877.
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During the traumatic opening decades of the Southern Sung, Emperor Kao-tsung’s unspoken determination to win imperial safety at any cost shaped not only court policy but Confucian intellectual developments. The intellectual climate of the Northern Sung had been confident, buoyant, outreaching, and exploratory; in the Southern Sung, it turned inward. The turn was not, however, a simple turn to conservative moral and political Confucianism; and in this book, James T. C. Liu explores how Kao-tsung used ideological window-dressing to consolidate extraordinary state power in the emperor’s hands. Ups and downs in the political fortunes of moralistic conservatives are also specially examined for their effects on the nature of the Neo-Confucianism that eventually became state orthodoxy.
BORN DEMON GOD CHAPTER 14 The True Cauldron of the Heart opened, and nine-colored divine light shot out from within, transforming into a nine-colored light pillar, breaking through the roof and flying straight up into the sky. Ning Xiaoxuan used an extremely fast technique to throw the Earth Core Rock Blood into the True Cauldron. Any Profound Pill that was contaminated by the “Earth Core Rock Blood” would immediately turn into a small Qilin, as if resurrected, flying out from the True Cauldron. The pill was shaped like a Qilin.