Uniqueness of two-parameter dyadic martingales and Walsh-Fourier series.
Walsh-Marcinkiewicz means and Hardy spaces
The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.
Weak-type estimates for the modified Hankel transform
We use the Galé and Pytlik [3] representation of Riesz functions to prove the Hörmander multiplier theorem for the modified Hankel transform.
Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series
Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights.
Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.
Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup
We obtain weighted boundedness, with weights of the type , δ > -1, for the maximal operator of the heat semigroup associated to the Laguerre functions, , when the parameter α is greater than -1. It is proved that when -1 < α < 0, the maximal operator is of strong type (p,p) if p > 1 and 2(1+δ)/(2+α) < p < 2(1+δ)/(-α), and if α ≥ 0 it is of strong type for 1 < p ≤ ∞ and 2(1+δ)/(2+α) < p. The behavior at the end points of the intervals where there is strong type is studied...
-Fluctuation and the Fourier–Walsh series of bounded functions.
Асимптотические свойства и васовые оценки для ортогональных многочленов Чебышёва-Хана
Исправления к работе 'О рядах по системе Хаара'
Наилучшие приближения функций в метрике полиномами Хаара и Уолша
Необходимые условия для множеств единственности рядов Уолша с лакунами
Непрерывная функция с расходящимися почти всюду кратным рядом Фурье по системе Уолша-Пэли
Непрерывные функции с монотонно убывающими коэффициентами Фурье по системе Хаара
О базисности системы Хаара в пространстве и принципе локализации в среднем
О восстановлении коэффициентов переставленного ряда Хаара
О гладкости примитивных Н.Н.Лузина и о теоремах Д.Е.Меньшова И Н.К.Бари
О коэффициентах Фурье по системе Хаара функций из пространств
О лакунарных рядах по мультипликативным системам функций. I
О линейных методах суммирования.
О некоторых классах множеств единственности кратных рядов Уолша