Related papers: The Geometry of the Dyadic Maximal Operator

We prove a sharp integral inequality for the dyadic maximal operator, connecting integrals of $\phi$, and of the dyadic maximal function of $\phi$.

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 prove a sharp integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables is possible, as can be seen in [3]. Our inequality of interest is proved…

We give an alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables, is possible. This last…

We prove a sharp multiparameter integral inequality for the dyadic maximal operator which refines the one-parameter inequality that is given by A.Melas in [4] which in turn is applied for the evaluation of the Bellman function of two…

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are…

We provide a description for the Bellman function related to the Carleson Imbedding theorem, first mentioned in [4], with the use of the Hardy operator.

In this paper we prove sharp Hardy inequalities by using Maximal function theory. Our results improve and extend the well-known results of G.Hardy \cite{Ha04}, T.Cazenave \cite {Ca03}, J.-Y.Chemin\cite {Ch06} and T.Tao\cite {TT06}.

We give a direct proof of the operator valued Hardy-Littlewood maximal inequality for $2<p<\infty$.

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…

In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and we construct explicit minimizers that satisfy the equality…

We define a generalized dyadic maximal operator involving the infinite product and discuss weighted inequalities for the operator. A formulation of the Carleson embedding theorem is proved. Our results depend heavily on a generalized…

We study properties for the sharp upper bound for integral quantities related to the Bellman function of three integral variables of the dyadic maximal operator, that is determined in [11].

We obtain sharp upper bounds for integral quantities related to the Bellman function of three integral variables of the dyadic maximal operator.

We compute the Bellman function of three integral variables associated to the dyadic maximal operator on a subset of its domain. Additionally, we provide an upper bound for the whole domain of its definition.

We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…

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…

In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy-Littlewood maximal operator associated to certain families of doubling, radial decreasing…

We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.

We obtain optimal generalized versions of Hardy inequalities, which as special cases contain Hardy's inequality and Hardy's inequality involving the distance function to the boundary of $ \Omega$. In addition we obtain neccesary and…