By Alexander Meskhi
This e-book is dedicated to the degree of non-compactness (essential norm) in weighted Lebesgue areas for maximal, power and singular operators dened, commonly conversing, on homogeneous teams. the most issues of the monograph comprise comparable effects for strength and singular integrals in weighted functionality areas with non-standard development. one of many major attribute beneficial properties of the monograph is that the issues are studied within the two-weighted environment and canopy the case of non-linear maps, corresponding to, Hardy-Littlewood and fractional maximal capabilities. ahead of, those difficulties have been investigated just for the limited type of kernel operators consisting in simple terms of Hardy-type and Riemann-Liouville transforms. The e-book should be regarded as a scientific and precise research of a category of particular vital operators from the boundedness/compactness or non-compactness viewpoint. the fabric is self-contained and will be learn by way of people with a few historical past in actual and useful research.
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