Suppose that η_1,...,η_n are measurable functions in L^2(R).We call the n-tuple(η_1,...,η_n) a Parseval super frame wavelet of length n if {2^(k/2) η_1(2~kt-l) ⊕···⊕2^(k/2) η_n(2~kt-l):k,l∈Z} is a Parseval frame for L^2(R)⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.
Let 0 ≤α < n,Ω be a rough kernel,and let A have derivatives of order m 1 in CBBMOq,μ2 with m ≥ 2.We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type,and obtain the boundedness of TΩA,α from the central Morrey spaces Ep,μ1 to Er,λ for λ = μ1 + μ2 + α/n and 1/r = 1/p + 1/q α/n.
In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.
In this paper, we will introduce multiresolution analysis with composite dilations and give a characterization of generator for multiresolution analysis with composite dilations.
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
Let V be a star shaped region.In 2006,Colzani,Meaney and Prestini proved that if function f satisfies some condition,then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere,when t goes to∞.In this paper we use a Theorem established by K.K.Chen to show that if we change their multiplier,then the condition on f can be weakened.
