The decompositional characterizations of the weighted Herz spaces on Rn are established. Using this decomposition, the boundedness on the weighted Herz spaces for a large class of sublinear operators is studied.
In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
Let Q 2 = [0, 1]2 be the unit square in two dimension Euclidean space ?2. We study the L p boundedness properties of the oscillatory integral operators T α,β defined on the set S(?3) of Schwartz test functions f by ...Let Q 2 = [0, 1]2 be the unit square in two dimension Euclidean space ?2. We study the L p boundedness properties of the oscillatory integral operators T α,β defined on the set S(?3) of Schwartz test functions f by $$ \mathcal{T}_{\alpha ,\beta } f(x,y,z) = \int_{Q^2 } {f(x - t,y - s,z - t^k s^j )e^{ - it^{ - \beta _1 } s^{ - \beta 2} } t^{ - 1 - \alpha _1 } s^{ - 1 - \alpha _2 } dtds} , $$ where β1 > α1 ? 0, β2 > α2 ? 0 and (k, j) ∈ ?2. As applications, we obtain some L p boundedness results of rough singular integral operators on the product spaces.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The decompositional characterizations of the weighted Herz spaces on Rn are established. Using this decomposition, the boundedness on the weighted Herz spaces for a large class of sublinear operators is studied.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金the National Natural Science Foundation of China (Grant Nos. 10571122, 10371046)the Natural Science Foundation of Fujian Province of China (Grant No. Z0511004)
文摘Let Q 2 = [0, 1]2 be the unit square in two dimension Euclidean space ?2. We study the L p boundedness properties of the oscillatory integral operators T α,β defined on the set S(?3) of Schwartz test functions f by $$ \mathcal{T}_{\alpha ,\beta } f(x,y,z) = \int_{Q^2 } {f(x - t,y - s,z - t^k s^j )e^{ - it^{ - \beta _1 } s^{ - \beta 2} } t^{ - 1 - \alpha _1 } s^{ - 1 - \alpha _2 } dtds} , $$ where β1 > α1 ? 0, β2 > α2 ? 0 and (k, j) ∈ ?2. As applications, we obtain some L p boundedness results of rough singular integral operators on the product spaces.
