Weierstrass transform associated with the Hankel operator.
Weighted bounded mean oscillation and the Hilbert transform
Weighted estimates for the Hankel-, - and - transformations
We give conditions on pairs of non-negative functions and which are sufficient that, for ,
Weighted inequalities for the Hilbert transform and the adjoint operator in the continuous case
Weighted inequalities through factorization.
In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined on X for which ||fw1/p||Lp(X) < ∞, where X is a measure space and w is a non-negative measurable function on X.It has recently...
Weighted norm inequalities for generalized Hankel conjugate transformations
Weighted norm inequalities for the -transformation.
Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions
Weighted-BMO and the Hilbert transform
In 1967, E. M. Stein proved that the Hilbert transform is bounded from to BMO. In 1976, Muckenhoupt and Wheeden gave an analogue of Stein’s result. They gave a necessary and sufficient condition for the boundedness of the Hilbert transform from . We improve the results of Muckenhoupt and Wheeden’s and give a necessary and sufficient condition for the boundedness of the Hilbert transform from to .
α-Mellin Transform and One of Its Applications
MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin transform...
Выпуклые оболочки и преобразование Лежандра
Гибридные интегральные преобразования Фурье- Вебера на оси с применением к задачам математической физики
Интегральные преобразования с ядрами типа Миттаг-Леффлера в классах ,
О двоичных аналогах операторов Харди и Харди-Литлвуда
О разложении произвольной функции в интеграл по присоединенным функциям Лежандра первого рода с комплексными значками
О разрешимости одной задачи интегральной геометрии
О формуле частичного и полного коммутирования операторов и , модельной формуле Грина и двойном преобразовании Лапласа
Об одном интегральном операторе свертки
Обращение одного интегрального оператора методом разложения по ортогональным операторам Ватсона
Потенциалы Рисса на пространствах Лоренца