A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from to when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.
An integral criterion for being an Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.
In [P] we characterize the pairs of weights for which the fractional integral operator of order from a weighted Lebesgue space into a suitable weighted and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...
This paper obtains a class of tight framelet packets on from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.
Let be the family of open rectangles in the plane ℝ² with a side of angle s to the x-axis. We say that a set S of directions is an R-set if there exists a function f ∈ L¹(ℝ²) such that the basis differentiates the integral of f if s ∉ S, and almost everywhere if s ∈ S. If the condition holds on a set of positive measure (instead of a.e.) we say that S is a WR-set. It is proved that S is an R-set (resp. a WR-set) if and only if it is a (resp. a ).