Premium
Some Applications of Gallagher's Theorem in Harmonic Analysis
Author(s) -
Stokolos A. M.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/33.2.210
Subject(s) - mathematics , simple (philosophy) , differentiable function , integrable system , harmonic function , function (biology) , locally integrable function , harmonic , pure mathematics , mathematical analysis , calculus (dental) , quantum mechanics , physics , medicine , philosophy , dentistry , epistemology , evolutionary biology , biology
We present a simple example of an integrable function for which the integral is not differentiable almost everywhere in the strong sense. A first example of such a function was given by S. Saks in 1935. Our construction is considerably more simple, due to the use of a remarkable theorem of P. X. Gallagher.