Fatou Type Theorems: Maximal Functions and Approach Regions - download pdf or read online

By Fausto Di Biase

ISBN-10: 0817639764

ISBN-13: 9780817639761

ISBN-10: 1461274966

ISBN-13: 9781461274964

A uncomplicated precept governing the boundary behaviour of holomorphic func­ tions (and harmonic services) is that this: less than sure development stipulations, for nearly each aspect within the boundary of the area, those services advert­ mit a boundary restrict, if we process the bounda-ry element inside of convinced process areas. for instance, for bounded harmonic services within the open unit disc, the normal strategy areas are nontangential triangles with one vertex within the boundary element, and fully inside the disc [Fat06]. in reality, those typical technique areas are optimum, within the experience that convergence will fail if we method the boundary within better areas, having a better order of touch with the boundary. the 1st theorem of this kind is because of J. E. Littlewood [Lit27], who proved that if we substitute a nontangential quarter with the rotates of any mounted tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that during Euclidean part­ areas (and the unit disc) there are in impression areas of convergence that aren't nontangential: those greater method areas comprise tangential sequences (as against tangential curves). The phenomenon came across by way of Nagel and Stein shows that the boundary behaviour of ho)omor­ phic features (and harmonic functions), in theorems of Fatou style, is regulated by means of a moment precept, which predicts the lifestyles of areas of convergence which are sequentially higher than the typical ones.

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Fatou Type Theorems: Maximal Functions and Approach Regions (Progress in Mathematics) by Fausto Di Biase

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