Download E-books Probabilistic Behavior of Harmonic Functions (Progress in Mathematics (Boston, Mass.), Vol. 175.) PDF

By Rodrigo Banuelos, Charles N. Moore

Harmonic research and chance have lengthy loved a collectively important courting that has been wealthy and fruitful. This monograph, geared toward researchers and scholars in those fields, explores a number of elements of this dating. the first concentration of the textual content is the nontangential maximal functionality and the realm functionality of a harmonic functionality and their probabilistic analogues in martingale idea. The textual content first offers the considered necessary history fabric from harmonic research and discusses identified effects in regards to the nontangential maximal functionality and region functionality, in addition to the principal and crucial function those have performed within the improvement of the field.The e-book subsequent discusses additional refinements of conventional effects: between those are sharp good-lambda inequalities and legislation of the iterated logarithm concerning nontangential maximal features and quarter services. Many purposes of those effects are given. all through, the consistent interaction among likelihood and harmonic research is emphasised and defined. The textual content includes a few new and plenty of fresh effects mixed in a coherent presentation.

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