Corpus ID: 237572162

# Fourier coefficients of functions in power-weighted $L_2$-spaces and conditionality constants of bases in Banach spaces

@inproceedings{Ansorena2021FourierCO,
title={Fourier coefficients of functions in power-weighted \$L\_2\$-spaces and conditionality constants of bases in Banach spaces},
author={Jos{\'e} L. Ansorena},
year={2021}
}
We prove that, given 2 < p < ∞, the Fourier coefficients of functions in L2(T, |t| dt) belong to lp, and that, given 1 < p < 2, the Fourier series of sequences in lp belong L2(T, |t| dt). Then, we apply these results to the study of conditional Schauder bases and conditional almost greedy bases in Banach spaces. Specifically, we prove that, for every 1 < p < ∞ and every 0 ≤ α < 1, there is a Schauder basis of lp whose conditionality constants grow as (m)m=1, and there is an almost greedy basis… Expand

#### References

SHOWING 1-10 OF 34 REFERENCES
Conditional quasi-greedy bases in Hilbert and Banach spaces
• Mathematics
• 2013
For quasi-greedy bases B in Hilbert spaces, we give an improved bound of the associated conditionality constants kN (B) = O(logN)1−e, for some e > 0, answering a question by Temlyakov. We show theExpand
On the existence of almost greedy bases in Banach spaces
• Mathematics
• 2003
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedyExpand
Lebesgue-Type Inequalities for Quasi-greedy Bases
• Mathematics
• 2011
We show that, for quasi-greedy bases in real or complex Banach spaces, an optimal bound for the ratio between greedy N-term approximation ∥x−GNx∥ and the best N-term approximation σN(x) is controlledExpand
On Approximate l1 Systems in Banach Spaces
• Computer Science, Mathematics
• J. Approx. Theory
• 2002
It is proved that certain lacunary Haar systems in L"1 are quasi-greedy basic sequences. Expand
On certain subspaces of $${\ell _p}$$ for $${0<p\le 1}$$ and their applications to conditional quasi-greedy bases in p-Banach spaces
• Mathematics
• 2019
We construct for each $0<p\le 1$ an infinite collection of subspaces of $\ell_p$ that extend the example from [J. Lindenstrauss, On a certain subspace of $\ell_{1}$, Bull. Acad. Polon. Sci. S\'er.Expand
An example of an almost greedy basis in L^1(0,1)
We give an explicit construction of an almost greedy basis of L 1 (0,1), complementing the results on existence of such a basis. The basis is described in terms of the Haar basis. We construct aExpand
Conditional Quasi-Greedy Bases in Non-superreflexive Banach Spaces
• Mathematics
• 2017
For a conditional quasi-greedy basis $$\mathcal {B}$$B in a Banach space, the associated conditionality constants $$k_{m}[\mathcal {B}]$$km[B] verify the estimate k_{m}[\mathcal {B}]={\mathcalExpand
A nonabsolute basis for Hilbert space
0<a <1/2, which is a basis for L2(-7r, 7r), but which is neither a Bessel nor a Hilbert basis, that is: 1. There is a y L2(-7r, 7r) such that y= n=O (Y, gn)fn, and ZGo (Ygn) 2 = 0 2. There is aExpand
Greedy approximation for biorthogonal systems in quasi-Banach spaces
• Mathematics
• 2019
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) inExpand
Topics in Banach space theory
• Mathematics
• 2006
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessibleExpand