Vol. 25, No. 3, 1968

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Mean values of power series

Thomas Muirhead Flett

Vol. 25 (1968), No. 3, 463–494

This paper gives a unified account of a body of work on mean values of functions regular in the unit disc, relating particularly to the fractional derivatives and integrals of such functions.

Two types of fractional derivative and integral are discussed. For each of the two types of fractional derivative considered, a function analogous to the Littlewood-Paley g-function is defined, and the properties of these two g-type functions are discussed. The results obtained here include several new inequalities, and, in particular, an extension (Theorem 5) of a theorem of Hirschman for indices less than or equal to 1.

Mathematical Subject Classification
Primary: 30.20
Received: 23 February 1967
Published: 1 June 1968
Thomas Muirhead Flett