By Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
The current quantity develops the speculation of integration in Banach areas, martingales and UMD areas, and culminates in a therapy of the Hilbert remodel, Littlewood-Paley concept and the vector-valued Mihlin multiplier theorem.
Over the prior fifteen years, inspired by way of regularity difficulties in evolution equations, there was great growth within the research of Banach space-valued capabilities and processes.
The contents of this huge and strong toolbox were more often than not scattered round in learn papers and lecture notes. Collecting this various physique of fabric right into a unified and obtainable presentation fills a niche within the present literature. The critical viewers that we have got in brain includes researchers who want and use research in Banach areas as a device for learning difficulties in partial differential equations, harmonic research, and stochastic research. Self-contained and providing whole proofs, this paintings is available to graduate scholars and researchers with a historical past in sensible research or comparable areas.