... Mathematics, 157 (2003), 647–688 The best constant for the centered Hardy-Littlewood maximal inequality By Antonios D Melas Abstract We find the exact value of the best possible constant C for the ... settling the problem of the computation of the best constant C completely We will prove the following Theorem For the centered Hardy-Littlewood maximal operator M , for every measure µ of the form ... constants in the case of centered maximal operators as described above, and the corresponding still open question raised there (see also [3, Problem 7.74b]), on whether the best constant in the...