Maximal inequality

We propose a new method for finding a zero point of a sum involving a Lipschitzian monotone operator and a maximally monotone operator, both acting on a real Hilbert space. The proposed method aims to extend forward-reflected-backward method by using inertial effect and variable metric. The weak convergence of the proposed method is proved under standard conditions.

11p viaburame 14-03-2025 1 1   Download

We find the exact value of the best possible constant C for the weak-type (1, 1) inequality for the one-dimensional centered Hardy-Littlewood maximal operator. We prove that C is the largest root of the quadratic equation 12C 2 − 22C + 5 = 0 thus obtaining C = 1.5675208 . . . . This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.

43p tuanloccuoi 04-01-2013 56 7   Download