arXiv subjects

Eleftherios N. Nikolidakis

Publications and source records attributed to Eleftherios N. Nikolidakis.

At least 19 recordsLinked to original sources

arXiv2025

A multiparameter integral inequality for the dyadic maximal operator and applications

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 integral variables for this maximal operator. Moreover we find the exact domain of definition of the related Bellman function of three integral variables and by using the results connected with the sharpness of this new multiparameter inequality we give lower bounds of this Bellman function.

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arXiv2025

A note on the Muckenhoupt class $A_1(\mathbb{R})$

We provide a direct proof of the best possible reverse Holder inequality satisfied by every weight defined on the interval $(0,1)$ with A1-constant equal to c > 1.

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arXiv2025

On a constant related to the Bellman function of three integral variables of the dyadic maximal operator: Part B

We study the behaviour of the constant that is provided in the articles [12] and [13], which is connected with the determination of the Bellman function of three integral variables of the dyadic maximal operator. More precisely we study the monotonicity properties of this constant with respect to the first variable from which it depends.

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arXiv2025

On a constant related to the Bellman function of three integral variables of the dyadic maximal operator: Part A

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arXiv2025

On a sharp upper bound related to the Bellman function of three integral variables of the dyadic maximal operator

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].

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arXiv2022

The Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem

We provide an alternative proof and expression of the Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem, which appears in [10]. We also evaluate the Bellman function of four variables of the dyadic maximal operator

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arXiv2022

An alternative approach to sharp $L^1$ estimates for the dyadic maximal operator

We prove sharp $L^1$ inequalities for the dyadic maximal function $M_Tϕ$ when $ϕ$ satisfies certain $L^1$ and $L^{\infty}$ conditions

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arXiv2019

A sharp integral inequality for the dyadic maximal operator and a related stability result

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 in this article by a simpler and more immediate way. We also study a stability result in connection with this inequality, that is we provide a necessary and sufficient condition, for a sequence of functions,under which we obtain equality in the limit. The proof of this result is based on the proof of the related inequality which we present in this article.

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arXiv2019

Properties of the Bellman function related to the Carleson Imbedding theorem for the dyadic maximal operator

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.

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arXiv2018

A refinement of a Hardy type inequality for negative exponents, and sharp applications to Muckenhoupt weights on R

We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on R. This work refines the results that appear in [9].

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arXiv2017

A second alternative approach for the study of the Muckenhoupt class $A_1(\mathbb{R})$

We find the exact best possible range of those $p > 1$ for which any function which belongs to $A_1(\mathbb{R})$, with $A_1$-constant equal to $c$, must also belong to $L^p$. In this way we provide alternative proofs of the results in [2] and [10].

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arXiv2017

Sharp integral inequalities for the dyadic maximal operator and applications

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

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arXiv2017

Sharp and general estimates for the Bellman function of three integral variables related to 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.

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arXiv2016

An alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator and applications

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 mentioned inequality, which was first noticed in [3],also generalizes in a certain direction the results of [7].

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arXiv2015

Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces

We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we introduce certain conditions on the weight that imply estimate for the maximal operator on the corresponding weighted space. Also using a well known estimate for the maximal operator by a double maximal operators on different m easures related to the weight we give new estimates for the above Bellman type functions.

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arXiv2015

Sharp Lorentz estimates for dyadic-like maximal operators and related Bellman functions

We precisely evaluate Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to local Lorentz type estimates. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we precisely evaluate the supremum of the Lorentz quasinorm of the maximal operator on a function $ϕ$ when the integral of $ϕ$ is fixed and also the same Lorentz quasinorm of $ϕ$ is fixed. Also we find the corresponding supremum when the integral of $ϕ$ is fixed and several weak type conditions are given.

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arXiv2015

Local lower norm estimates for dyadic maximal operators and related Bellman functions

We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous tree-like families in probability spaces.

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arXiv2014

A Hardy inequality and applications to reverse Holder inequalities for weights on $R$

We prove a sharp integral inequality valid for non-negative functions defined on $[0,1]$, with given $L^1$ norm. This is in fact a generalization of the well known integral Hardy inequality. We prove it as a consequence of the respective weighted discrete analogue inequality which proof is presented in this paper. As an application we find the exact best possible range of $p>q$ such that any non-increasing $f$ which satisfies a reverse Hölder inequality with exponent $q$ and constant $c$ upon the subintervals of $[0,1]$, should additionally satisfy a reverse Hölder inequality with exponent $p$ and a different in general constant $c'$. The result has been treated in \cite{1} but here we give an alternative proof based on the above mentioned inequality.

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