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Random series in Lp(X, Σ,μ) using unconditional basic sequences and lp stable sequences: A result on almost sure almost everywhere convergence
(American Mathematical Society, 2007-11)
Here we study the almost sure almost everywhere convergence of random series of the form Σ∞ i=1αifi in the Lebesgue spaces L p(X, Σ,μ), where the ai's are centered random variables, and the fi's constitute an unconditional ...
Nonnegative trigonometric polynomials
(2002-12-01)
An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative ...
Nonnegative trigonometric polynomials
(2002-12-01)
An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative ...
Differential transforms in weighted spaces
(Birkhauser Boston Inc, 2006-02)
We extend the results by Jones and Rosenblatt about the series of the differences of differentiation operators along lacunary sequences to BMO and to the setting of weighted Lp spaces. We use a different approach which ...
An extremal nonnegative sine polynomial
(2003-09-01)
For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed ...
An extremal nonnegative sine polynomial
(2003-09-01)
For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed ...
A convergence result for unconditional series in Lp(u)
(2013-12)
We give sufficient conditions for the convergence almost everywhere of the expansion with respect to an unconditional basis for<br />functions in Lp, p ≥ 2. This result extends the classical theorem of<br />Menchoff and ...
Multiparameter ergodic Cesàro-α averages
(Polish Academy of Sciences. Institute of Mathematics, 2015-03)
Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages
Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏ ...