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### A class of Fourier series

Colloquium Mathematicae

Acta Arithmetica

### A new extension of monotone sequences and its applications.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A note on a theorem of Boas

Matematički Vesnik

### A note on Fourier coefficients

Rendiconti del Seminario Matematico della Università di Padova

### A Note on Lipschitz Classes.

Mathematische Zeitschrift

### A note on rearrangements of Fourier coefficients

Annales de l'institut Fourier

Let $f\left(x\right)\sim \Sigma {a}_{n}{e}^{2\pi inx},f*\left(x\right)\sim {\sum }_{n=0}^{\infty }a{*}_{n}\phantom{\rule{0.166667em}{0ex}}\mathrm{cos}\phantom{\rule{0.166667em}{0ex}}2\pi nx$, where the $a{*}_{n}$ are the numbers $|{a}_{n}|$ rearranged so that ${a}_{n}^{*}↘0$. Then for any convex increasing $\psi$, $\parallel \psi \left(|f{|}^{2}{\parallel }_{1}\le \parallel \psi \left(20|f*{|}^{2}{\parallel }_{1}$. The special case $\psi \left(t\right)={t}^{q/2}$, $q\ge 2$, gives $\parallel f{\parallel }_{q}\le 5\parallel f*{\parallel }_{q}$ an equivalent of Littlewood.

### A remark on entropy of Abelian groups and the invariant uniform approximation property

Studia Mathematica

### A simple observation about compactness and fast decay of Fourier coefficients.

Annals of Functional Analysis (AFA) [electronic only]

### A study of the real Hardy inequality.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### A theorem for Fourier coefficients of a function of class ${L}^{p}$.

International Journal of Mathematics and Mathematical Sciences

### A theorem of Cesari on mulitple Fourier series

Studia Mathematica

### A variation norm Carleson theorem

Journal of the European Mathematical Society

We strengthen the Carleson-Hunt theorem by proving ${L}^{p}$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $r>\mathrm{𝚖𝚊𝚡}\left\{{p}^{\text{'}},2\right\}$. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.

### Addition au mémoire sur les fonctions discontinues

Annales scientifiques de l'École Normale Supérieure

### Algebrability of the set of non-convergent Fourier series

Studia Mathematica

We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

### An application of interpolation theory to Fourier series

Studia Mathematica

### An approximation problem in ${L}^{p}\left(\left[0,2\pi \right]\right)$, 2 < p < ∞

Studia Mathematica

### An estimate of the Fourier coefficients of functions belonging to the Besov class.

Publications de l'Institut Mathématique. Nouvelle Série

### An extension of the Riemann-Lebesgue lemma and some applications.

Acta Universitatis Apulensis. Mathematics - Informatics

### An inverse Sidon type inequality

Studia Mathematica

Sidon proved the inequality named after him in 1939. It is an upper estimate for the integral norm of a linear combination of trigonometric Dirichlet kernels expressed in terms of the coefficients. Since the estimate has many applications for instance in ${L}^{1}$ convergence problems and summation methods with respect to trigonometric series, newer and newer improvements of the original inequality has been proved by several authors. Most of them are invariant with respect to the rearrangement of the coefficients....

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