arXiv subjects
Publications and source records attributed to Eleftherios Nikolidakis.
We obtain sharp upper bounds for integral quantities related to the Bellman function of three integral variables of the dyadic maximal operator.
We prove that the extremal sequences for the Bellman function of the dyadic maximal operator behave approximately as eigenfunctions of this operator for a specific eigenvalue. We use this result to prove the analogous one with respect to the Hardy operator.
We give a characterization of the extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality. In fact we prove that they behave approximately like eigenfunctions of this operator for a specific eigenvalue. For this approach we use the one introduced in [4], where the respective Bellman function has been precisely evaluated.
We give a characterization of the extremal sequences for the Bellman function of the dyadic maximal operator.In fact we prove that they behave approximately like eigenfunctions of this operator for a specific eigenvalue.
We obtain sharp estimates for the localized distribution function of Mϕ, when ϕbelongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.
We prove a sharp integral inequality for the dyadic maximal operator and give as an application another proof for the computation of its Bellman function of three variables.
We precisely compute the Bellman function of two variables of the dyadic maximal operator in relation to Kolmogorov inequality. In this way we give an alternative proof of the results in [5].Additionally, we characterize the sequences of functions that are extremal for this Bellman function.The proof of this is based on that is given in this paper for the Bellman function we are interested in.
We prove a sharp integral inequality which connects the dyadic maximal operator with the Hardy operator. We also give some applications of this inequality.
We prove that the decreasing rearrangement of a dyadic A1 weight w with dyadic A1 constant [w]_{1,T}=c with respect to a tree T of homogeneity k,on a non-atomic probability space, is a usual A1 weight on (0,1] with A1 constant not more than kc-k+1.We prove also that the result is sharp, when one considers all such weights w.
We prove a necessary condition that has every extremal sequence for the Bellman function of the dyadic maximal operator.This implies the weak-Lp uniqueness for such a sequence.
We provide sharp weak estimates for the distribution function of Mϕwhen on ϕwe impose L1, Lq and Lp,1 restrictions. Here M is the dyadic maximal operator associated to a tree T on a non-atomic probability measure space.