Eleftherios N. Nikolidakis

activity

20102025

most citedA sharp integral rearrangement inequality for the dyadic maximal operator and applications

4 citations · 12 across the 25 of their papers we have counts for

collaborators

35 papers

math.FA2025

A note on the Muckenhoupt class $A_{1} (R)$

Eleftherios N. Nikolidakis, Andreas G. Tolias

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.

math.CA2025

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

Eleftherios N. Nikolidakis

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…

math.CA2025

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

Eleftherios N. Nikolidakis

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…

math.CA2024

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

Eleftherios N. Nikolidakis

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…

math.CA2023

Sharp upper bounds for integral quantities related to the Bellman function of three variables of the dyadic maximal operator

Eleftherios Nikolidakis

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

math.CA2021

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

Eleftherios N. Nikolidakis, Andreas G. Tolias

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

math.FA2019

A multiparameter integral inequality for the dyadic maximal operator and applications

Eleftherios N. Nikolidakis

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 appl…

math.FA2018★ 1 cited

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

Eleftherios N. Nikolidakis, Theodoros Stavropoulos

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 Mu…

math.FA2018

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

Eleftherios N. Nikolidakis

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.

math.FA2017

A second alternative approach for the study of the Muckenhoupt class $A_{1} (R)$

Eleftherios N. Nikolidakis

We find the exact best possible range of those $p > 1$ for which any function which belongs to $A_{1} (R)$ , with $A_{1}$ -constant equal to $c$ , must also belong to $L^{p}$ . In th…

math.FA2017

Sharp and general estimates for the Bellman function of three integral variables related to the dyadic maximal operator

Anastasios D. Delis, Eleftherios N. Nikolidakis

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 who…

math.FA2016

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

Eleftherios N. Nikolidakis

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,…

math.CA2016

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

Eleftherios N. Nikolidakis

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 operato…

math.FA2015

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

Antonios D. Melas, Eleftherios N. Nikolidakis, Dimitrios Cheliotis

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…

math.CA2015

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

Antonios D. Melas, Eleftherios N. Nikolidakis

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 actuall…

math.FA2015

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

Antonios D. Melas, Eleftherios N. Nikolidakis

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 o…

math.FA2015

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

Eleftherios N. Nikolidakis

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…

math.CA2015

Sharp integral inequalities for the dyadic maximal operator and applications

Anastasios D. Delis, Eleftherios N. Nikolidakis

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

math.CA2014

Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on $[0, 1]^{n}$ and rearrangements of functions

Eleftherios N. Nikolidakis

We introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0, 1]^{n}$ and study the behavior of the nonincreasing rearrangement of $f$ , as an element of the…

math.FA2014★ 2 cited

Dyadic weights on $R^{n}$ and reverse Holder inequalities

Eleftherios N. Nikolidakis, Antonios D. Melas

We prove that for any weight $ϕ$ defined on $[0, 1]^{n}$ that satisfies a reverse Holder inequality with exponent p > 1 and constant $c \geq 1$ upon all dyadic subcubes of $[0, 1]^{n}$ , it'…

math.FA2013★ 1 cited

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

Eleftherios N. Nikolidakis

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 i…

math.FA2013

A sharp integral Hardy type inequality and applications to Muckenhoupt weights on $R$

Eleftherios N. Nikolidakis

We prove a generalization of a Hardy type inequality for negative exponents valid for non-negative functions defined on $(0, 1]$ . As an application we find the exact best possible r…

math.FA2013

$A_{1}$ weights on $R$ , an alternative approach

Eleftherios N. Nikolidakis

We will prove that if $ϕ$ belongs to the class $A_{1} (R)$ with constant $c \geq 1$ then the decreasing rearrangement of $ϕ$ , belongs to the same class with constant not more than $c$ .…

math.FA2013★ 2 cited

Extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality

Eleftherios Nikolidakis

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 p…

A note on the Muckenhoupt class A1​(R)

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

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

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

Sharp upper bounds for integral quantities related to the Bellman function of three variables of the dyadic maximal operator

An alternative approach to sharp L1 estimates for the dyadic maximal operator

A multiparameter integral inequality for the dyadic maximal operator and applications

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

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

A second alternative approach for the study of the Muckenhoupt class A1​(R)

Sharp and general estimates for the Bellman function of three integral variables related to the dyadic maximal operator

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

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

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

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

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

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

Sharp integral inequalities for the dyadic maximal operator and applications

Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on [0,1]n and rearrangements of functions

Dyadic weights on Rn and reverse Holder inequalities

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

A sharp integral Hardy type inequality and applications to Muckenhoupt weights on R

A1​ weights on R, an alternative approach

Extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality

A note on the Muckenhoupt class $A_{1} (R)$

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

A second alternative approach for the study of the Muckenhoupt class $A_{1} (R)$

Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on $[0, 1]^{n}$ and rearrangements of functions

Dyadic weights on $R^{n}$ and reverse Holder inequalities

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

A sharp integral Hardy type inequality and applications to Muckenhoupt weights on $R$

$A_{1}$ weights on $R$ , an alternative approach