On the mean modulus of an analytic function

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On the Mean Modulus of an Analytic Function

For fixed ƒ and r this mean modulus Mt(r;f) as a function of / is continuous, nonnegative, nondecreasing, and is bounded above by the maximum modulus of ƒ on C(r) [l, 2 ] . 1 Therefore the limit of Mt(r;f) exists as /—>0 and /—» oo. This limit is defined to be the mean modulus of ƒ on C(r) of order 0 and of order oo respectively. I t may be shown that the mean modulus of order 0 is the geometri...

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1949

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1949-09197-8