Weighted $L^p$-boundedness of Fourier series with respect to generalized Jacobi weights

Hernández, José Javier Guadalupe; Riera, Mario Pérez; Blasco, Francisco; Malumbres, Juan

doi:10.5565/publmat_35291_08

Cited by 4 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A general result including weights for Jacobi expansions can be seen in [9]. In [3], by applying the boundedness with weights of the Hilbert transform, the authors did a complete study of the boundedness of the partial sum operators related to generalized Jacobi weights. The same authors studied the generalized Jacobi weights with mass points on the interval [−1, 1] (see [4]).…”

Section: Introductionmentioning

confidence: 99%

Fourier Series of Gegenbauer-Sobolev Polynomials

Ciaurri¹,

Mínguez²

2018

SIGMA

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Fourier Series of Gegenbauer-Sobolev Polynomials

Ciaurri¹,

Mínguez²

2018

SIGMA

View full text Add to dashboard Cite

show abstract

“…A general result including weights for Jacobi expansions can be seen in [10]. In [4], by applying the boundedness with weights of the Hilbert transform, the authors did a complete study of the boundedness of the partial sum operators related to generalized Jacobi weights. The same authors studied the generalized Jacobi weights with mass points on the interval [−1, 1] (see [5]).…”

Section: Introductionmentioning

confidence: 99%

Fourier series of Jacobi–Sobolev polynomials

Ciaurri

Ceniceros

2018

Integral Transforms and Special Functions

View full text Add to dashboard Cite

Let {q (α,β,m) n (x)} n≥0 be the orthonormal polynomials respect to the Sobolev-type inner product f, g α,β,m = m k=0 1 −1We obtain necessary and sufficient conditions for the uniform boundedness of the partial sum operators related to this sequence of polynomials in the Sobolev space W p,m α,β . As a consequence we deduce the convergence of such partial sums in the norm of W p,m α,β .2010 Mathematics Subject Classification. Primary: 42A20. Secondary: 33C47. Key words and phrases. Sobolev-type inner product, Sobolev polynomials, Jacobi polynomials, partial sum operator.

show abstract

Weighted norm inequalities for polynomial expansions associated to some measures with mass points

et al. 1996

Self Cite

View full text Add to dashboard Cite

Abstract. Fourier series in orthogonal polynomials with respect to a measure ν on [−1, 1] are studied when ν is a linear combination of a generalized Jacobi weight and finitely many Dirac deltas in [−1, 1]. We prove some weighted norm inequalities for the partial sum operators Sn, their maximal operator S * and the commutator [M b , Sn], where M b denotes the operator of pointwise multiplication by b ∈ BMO. We also prove some norm inequalities for Sn when ν is a sum of a Laguerre weight on R + and a positive mass on 0. Introduction.Let ν be a positive Borel measure on R with infinitely many points of increase and such that all the momentsare finite. For each suitable function f , let S n f denote the n-th partial sum of the Fourier expansion of f with respect to the system of orthogonal polynomials associated to dν. The uniform boundedness of the operators S n : Let us consider for simplicity the unweighted case. For a generalized Jacobi weight, not only the uniform boundedness of the operators S n has been studied, but also that of the maximal operator S * defined by1991 Mathematics Subject Classification. Primary 42C10.

show abstract

Weighted $L^p$-boundedness of Fourier series with respect to generalized Jacobi weights

Cited by 4 publications

References 13 publications

Fourier Series of Gegenbauer-Sobolev Polynomials

Fourier Series of Gegenbauer-Sobolev Polynomials

Fourier series of Jacobi–Sobolev polynomials

Weighted norm inequalities for polynomial expansions associated to some measures with mass points

Contact Info

Product

Resources

About