Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.
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
We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especial...We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.展开更多
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）...We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.展开更多
文摘Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.
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.
基金supported by National Natural Science Foundation of China(Grant Nos.113712951102610411471041 and 11471288)
文摘We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371295, 11471041 and 11526122)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ053)+2 种基金Research Award Fund for Outstanding Young Scientists of Shandong Province (Grant No. BS2015SF012)Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01)Natural Science Foundation of Fujian Province of China (Grant No. 2015J01025)
文摘We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.
