# An inverse Sidon type inequality

Studia Mathematica (1993)

- Volume: 105, Issue: 3, page 283-308
- ISSN: 0039-3223

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topFridli, S.. "An inverse Sidon type inequality." Studia Mathematica 105.3 (1993): 283-308. <http://eudml.org/doc/216000>.

@article{Fridli1993,

abstract = {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. Although the newest results are close to best possible, no nontrivial lower estimate has been given so far. The aim of this paper is to give the best rearrangement invariant function of coefficients that can be used in a Sidon type inequality. We also show that it is equivalent to an Orlicz type and a Hardy type norm. Examples of applications are also given.},

author = {Fridli, S.},

journal = {Studia Mathematica},

keywords = {Sidon type inequalities; Hardy spaces; convergence classes; Hardy space; trigonometric Dirichlet kernels; best rearrangement invariant function of coefficients; Sidon type inequality},

language = {eng},

number = {3},

pages = {283-308},

title = {An inverse Sidon type inequality},

url = {http://eudml.org/doc/216000},

volume = {105},

year = {1993},

}

TY - JOUR

AU - Fridli, S.

TI - An inverse Sidon type inequality

JO - Studia Mathematica

PY - 1993

VL - 105

IS - 3

SP - 283

EP - 308

AB - 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. Although the newest results are close to best possible, no nontrivial lower estimate has been given so far. The aim of this paper is to give the best rearrangement invariant function of coefficients that can be used in a Sidon type inequality. We also show that it is equivalent to an Orlicz type and a Hardy type norm. Examples of applications are also given.

LA - eng

KW - Sidon type inequalities; Hardy spaces; convergence classes; Hardy space; trigonometric Dirichlet kernels; best rearrangement invariant function of coefficients; Sidon type inequality

UR - http://eudml.org/doc/216000

ER -

## References

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