On Khintchine type inequalities for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" id="mml1" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-wise independent Rademacher random variables

Pass, Brendan; Spektor, Susanna

doi:10.1016/j.spl.2017.09.002

Cited by 11 publications

(9 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is of Hanner cotype (1,3). Thus, besides L 1 norm, there are many other norms (like the norm induced by the support function of a zonoid) is of Hanner cotype (1,3). Furthermore, by Witsenhausen's result [15], we know that a hypermetric normed space is of Hanner cotype (1, n) for any n ∈ Z + .…”

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

“…is of Hanner cotype (1,3). Thus, besides L 1 norm, there are many other norms (like the norm induced by the support function of a zonoid) is of Hanner cotype (1,3).…”

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

“…Remark 2. In the case of the real line R, Astashkin showed a better estimate than Theorem 1 (3) (see [16]).…”

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

“…where (v 1 , • • • , v n ) ∈ R n , and {ǫ i } n i=1 is a sequence of independent random variables in Rademacher distribution. Khintchine inequality attracts much attentions from various fields, particularly in probability, functional analysis and combinatorics (see [2,3,4,5,6,7,8,9]). We specially refer the readers to the systematical works by Astashkin [4,5,8,9,16].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Khintchine inequality on normed spaces and the application to Banach-Mazur distance

Luo,

Zhang

2020

Preprint

View full text Add to dashboard Cite

We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is replaced by general symmetric distributions. The proof involves the p-barycenter and Birkhoff's ergodic theorem. More importantly, by employing these Khintchine inequalities, we get some lower bounds for Banach-Mazur distance between l p -ball and a general centrally symmetric convex body.

show abstract

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

“…is of Hanner cotype (1,3). Thus, besides L 1 norm, there are many other norms (like the norm induced by the support function of a zonoid) is of Hanner cotype (1,3).…”

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

“…Remark 2. In the case of the real line R, Astashkin showed a better estimate than Theorem 1 (3) (see [16]).…”

Section: Khintchine-type Inequalities On Normed Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Khintchine inequality on normed spaces and the application to Banach-Mazur distance

Luo,

Zhang

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…See [17,23] for some previous Hoeffding-type inequalities for sums of R-wise independent random variables.…”

mentioning

confidence: 99%

The Ionescu–wainger Multiplier Theorem and the Adeles

Tao

2021

Mathematika

View full text Add to dashboard Cite

The Ionescu-Wainger multiplier theorem establishes good L p bounds for Fourier multiplier operators localized to major arcs; it has become an indispensible tool in discrete harmonic analysis. We give a simplified proof of this theorem with more explicit constants (removing logarithmic losses that were present in previous versions of the theorem), and give a more general variant involving adelic Fourier multipliers. We also establish a closely related adelic sampling theorem that shows that p (Z d ) norms of functions with Fourier transform supported on major arcs are comparable to the L p (A d Z ) norm of their adelic counterparts. §1. Introduction. This paper will be concerned with the L p theory of Fourier multiplier operators on various locally compact abelian groups, such as Z d , R d , andIn order to treat these groups in a unified fashion, we adopt the following abstract harmonic analysis notation. Definition 1.1 (Pontryagin duality). An LCA group is a locally compact abelian group G = (G, +) equipped with a Haar measure μ G . A Pontryagin dual of an LCA group G is an LCA group G * = (G * , +) with a Haar measure μ G * and a continuous bihomomorphism (x, ξ ) → x • ξ (which we call a pairing) from G × G * to the unit circle T = R/Z, such that the Fourier transformwhere e : T → C is the standard character e(θ ) := e 2πiθ , extends to a unitary map from L 2 (G) to L 2 (G * ); in particular, we have the Plancherel identityfor all f ∈ L 2 (G), as well as the inversion formulaIf ⊂ G * is measurable, we say that f ∈ L 2 (G) is Fourier supported in if F G f vanishes outside of (modulo null sets). The space of such functions will be denoted L 2 (G) .If m ∈ L ∞ (G * ), we define the associated Fourier multiplier operator T m : L 2 (G) → L 2 (G) by the formulaWe refer to m as the symbol of T m .

show abstract

Sharp Khinchin-type inequalities for symmetric discrete uniform random variables

Havrilla

Tkocz

2021

Isr. J. Math.

View full text Add to dashboard Cite

On Khintchine type inequalities fork-wise independent Rademacher random variables

Cited by 11 publications

References 8 publications

Khintchine inequality on normed spaces and the application to Banach-Mazur distance

Khintchine inequality on normed spaces and the application to Banach-Mazur distance

The Ionescu–wainger Multiplier Theorem and the Adeles

Sharp Khinchin-type inequalities for symmetric discrete uniform random variables

Contact Info

Product

Resources

About