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This book gives a thorough and self contained presentation of H1, its known isomorphic invariants and a complete classification of H1 on spaces of homogeneous type. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.
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The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.
The X-H1 in plain English! Written for Fujifilm's outstanding X-H1 camera, this is This is EVERYTHING X-H1 explained in easy to understand language! It is the Manual on Steroids and much more... In it, I assume you are a photographer, so I don't dive in to the basics of photography (except in an Appendix). Everything comes with clear tutorials and examples. So if you're uncertain about anything your X-H1 does, grab this book! It's packed with clear tutorials and examples, with over 900 tips, tricks, and tweaks to help you master photography with your X-H1.
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