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- W2090779078 abstract "If h is measurable on a measure space M with measure m, its distribution function is defined for y>O by X7,(y) =X(y) =m {xEM; f(x) >y. The nonincreasing rearrangement of h onto (0, oo) is then the function given by h*(t) =inf {y>0; X(y) O. Both h* and X are non-negative and nonincreasing functions that are continuous from the right. h* and h have the same distribution function, thus ||h*||p =-|h1HP. Moreover, supu>0y {X(y) } 1/=supt>o tllqh*(t). Consequently the theorem of Marcinkiewicz can be stated in the following way: Suppose T is quasi-linear2 and, for 1 oo, i=O, 1, with Po<pi, qo5qi," @default.
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- W2090779078 date "1964-06-01" @default.
- W2090779078 modified "2023-09-27" @default.
- W2090779078 title "The Marcinkiewicz interpolation theorem" @default.
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- W2090779078 doi "https://doi.org/10.1090/s0002-9939-1964-0169038-4" @default.
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