Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights

Pointwise bounds of orthogonal expansions on the real line via weighted Hilbert transforms

“…The first significant results dealing with mean convergence of orthonormal expansions on the line are due to Askey and Wainger for the Hermite weight w(x) = exp(−x 2 ), see [1]. Thereafter, followed related results of Muckenhoupt, see [24,25], Mhaskar and Xu, see [23] and Jha and Lubinsky, see [14].…”

“…More precisely, we will use Pollards decomposition of K as applied by Askey and Wainger, Muckenhoupt, Mhaskar and Xu, and Jha and Lubinsky in [1], [24,25], [23] and [14]. For a given t, x ∈ R, write,…”

“…Analogues of theorem 1 in L p (1 < p < ∞) are contained in[1,4,14,[23][24][25]. More precisely, in[1,24,25], Askey, Waigner and Muckenhoupt proved an L p analogue of theorem 1 for the Hermite weight ((1.6) with α = 2).…”

Hermite-Fejér and Grünwald interpolation at generalized Laguerre zeros

“…By the latter relation it follows that the function Q (x) has an algebraic increasing behaviour [7,Lemma 4.1 (a)].…”

Some Fourier-type operators for functions on unbounded intervals

“…Subsequently, B. Muckenhoupt [15] introduced the weights u(x) = 1 + |x| b w(x) and v(x) = 1 + |x| B 1 + log + |x| η w(x), with w(x) = e −x 2 , and thus he proved inequalities of the type (1.1) S. W. Jha and D. S. Lubinsky [6] extended the results of B. Muckenhoupt to the case of Freud weights, namely they replaced w(x) = e −x 2 by w(x) = e −Q(x) (under suitable assumptions on Q).…”