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

(12 reference statements)

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“…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

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Section: Introductionmentioning

confidence: 99%

Fourier Series of Gegenbauer-Sobolev Polynomials

Ciaurri¹,

Mínguez²

2018

SIGMA

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“…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

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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.

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

et al. 1996

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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.

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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

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