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

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26 papers · 1 filter

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.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.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.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.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…

math.FA2013

The Bellman function of the dyadic maximal operator related to Kolmogorov's inequality

Eleftherios Nikolidakis

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 resu…

math.FA2013

Extremal sequences for the Bellman function of the dyadic maximal operator and applications to the Hardy operator

Eleftherios Nikolidakis

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 u…

math.FA2013★ 4 cited

A sharp integral rearrangement inequality for the dyadic maximal operator and applications

Eleftherios Nikolidakis, Antonios Melas

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.

math.FA2013★ 1 cited

Extremal sequences for the Bellman function of the dyadic maximal operator

Eleftherios Nikolidakis

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…

math.FA2012

Dyadic A1 weights and equimeasurable rearrangements of functions

Eleftherios Nikolidakis

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,…

math.FA2012

The Bellman function of two variables for the dyadic maximal operator

Eleftherios N. Nikolidakis, Antonios D. Melas

For p>1 we find the Bellman function of two variables associated with the dyadic maximal operator on Rn.Actually we do that in the more general setting of tree-like maximal operato…

math.FA2011

Properties of extremal sequences for the Bellman function of the dyadic maximal operator

Eleftherios Nikolidakis

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.

math.FA2011

The Geometry of the Dyadic Maximal Operator

Eleftherios Nikolidakis

We prove a sharp integral inequality which connects the dyadic maximal operator with the Hardy operator. We also give some applications of this inequality.

math.FA2010

Optimal weak type estimates for dyadic-like maximal operators

Eleftherios Nikolidakis

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 note on the Muckenhoupt class A1​(R)

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

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

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

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

The Bellman function of the dyadic maximal operator related to Kolmogorov's inequality

Extremal sequences for the Bellman function of the dyadic maximal operator and applications to the Hardy operator

A sharp integral rearrangement inequality for the dyadic maximal operator and applications

Extremal sequences for the Bellman function of the dyadic maximal operator

Dyadic A1 weights and equimeasurable rearrangements of functions

The Bellman function of two variables for the dyadic maximal operator

Properties of extremal sequences for the Bellman function of the dyadic maximal operator

The Geometry of the Dyadic Maximal Operator

Optimal weak type estimates for dyadic-like maximal operators

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

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

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