Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology refe...Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology referred to as doubly multiple parameters weighted fractional Fourier transform(DMWFRFT), which can strengthen the physical layer security of wireless communication. This paper introduces the concept of DM-WFRFT based on multiple parameters WFRFT(MP-WFRFT), and then presents its four properties. Based on these properties, the parameters decryption probability is analyzed in terms of the number of parameters. The number of parameters for DM-WFRFT is more than that of the MP-WFRFT,which indicates that the proposed scheme can further strengthen the the physical layer security. Lastly, some numerical simulations are carried out to illustrate that the efficiency of proposed DM-WFRFT is related to preventing eavesdropping, and the effect of parameters variety on the system performance is associated with the bit error ratio(BER).展开更多
Let M be the multilinear maximal function and = （b1, . . . , bm） be a collection of locally integrable functions. Denote by M and [,M] the maximal commutator and the commutator of M with , respectively. In this pape...Let M be the multilinear maximal function and = （b1, . . . , bm） be a collection of locally integrable functions. Denote by M and [,M] the maximal commutator and the commutator of M with , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M and [,M] are studied. Some characterizations of the class of functions bj are given, for which these operators satisfy some strong or weak type estimates.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
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular in...This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.展开更多
By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.
Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. As a result, we perfect and generalize the previous conclusions given by H. Bercovici, ...Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. As a result, we perfect and generalize the previous conclusions given by H. Bercovici, C. Foias, and C. Pearcy. Moreover, we remark that Question 21 posed by Shields has been negatively answered.展开更多
In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essential...In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.展开更多
In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfi...In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.展开更多
Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-...Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.展开更多
An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss,which is equipped with a measure satisfying an additional reverse doubling property.In this paper we study the boundedness of multilinear ...An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss,which is equipped with a measure satisfying an additional reverse doubling property.In this paper we study the boundedness of multilinear singular integral operators in weighted Morrey spaces within the framework of RD-spaces.展开更多
A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and ...A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and only if A and B are unitarily equivalent.We also study the reducing subspaces of A^kI+IB^l and give some examples.As an application,we study the reducing subspaces of multiplication operators Mzk+αωl on function spaces.展开更多
It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥...It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥1,where ansatisfiesan=1.In[8],the author obtainedsimilar result for the hyponormal weighted unilateral shift of multiplicity 2.The aim of this展开更多
Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）d...Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）dξ1dξ2︱^2dt/t）^1/2.Let s be an integer with s ∈ [n ＋ 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p） and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p（νω） if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 ＋ 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p,∞（νω）. The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before.展开更多
We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniquen...We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.展开更多
文摘Enhancing the security of the wireless communication is necessary to guarantee the reliable of the data transmission, due to the broadcast nature of wireless channels. In this paper, we provide a novel technology referred to as doubly multiple parameters weighted fractional Fourier transform(DMWFRFT), which can strengthen the physical layer security of wireless communication. This paper introduces the concept of DM-WFRFT based on multiple parameters WFRFT(MP-WFRFT), and then presents its four properties. Based on these properties, the parameters decryption probability is analyzed in terms of the number of parameters. The number of parameters for DM-WFRFT is more than that of the MP-WFRFT,which indicates that the proposed scheme can further strengthen the the physical layer security. Lastly, some numerical simulations are carried out to illustrate that the efficiency of proposed DM-WFRFT is related to preventing eavesdropping, and the effect of parameters variety on the system performance is associated with the bit error ratio(BER).
基金Supported by National Natural Science Foundation of China(Grant No.11271162)the Scientific Research Fund of Heilongjiang Provincial Education Department(Grant No.12531720)the Scientific Research Fund of Mudanjiang Normal University(Grant No.GY201305)
文摘Let M be the multilinear maximal function and = （b1, . . . , bm） be a collection of locally integrable functions. Denote by M and [,M] the maximal commutator and the commutator of M with , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M and [,M] are studied. Some characterizations of the class of functions bj are given, for which these operators satisfy some strong or weak type estimates.
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This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 10961015, 11261023, 10871024, 10931001, 11561057） and the Key Laboratory of Mathematics and Complex System, Ministry of Education, China.
文摘This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11371316, 11271330, 11571306）.
文摘By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.
文摘Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. As a result, we perfect and generalize the previous conclusions given by H. Bercovici, C. Foias, and C. Pearcy. Moreover, we remark that Question 21 posed by Shields has been negatively answered.
基金supported by the National Natural Science Foundation of China(Nos.11871101,12171399)NSFC-DFG(No.11761131002)+3 种基金the Natural Science Foundation of Fujian Province(No.2021J05188)the Scientific Research Project of The Education Department of Fujian Province(No.JAT200331)the President’s fund of Minnan Normal University(No.KJ2020020)the Institute of Meteorological Big Data-Digital Fujian,Fujian Key Laboratory of Data Science and Statistics and Fujian Key Laboratory of Granular Computing and Applications(Minnan Normal University)。
文摘In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.
基金Supported partially by the National Natural Science Foundation of China(Grant No.11371200)the Research Fund for the Doctoral Program of Higher Education(Grant No.20120031110023)
文摘In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.
基金supported by National Natural Science Foundation of China(Grant Nos.11301534 and 11571039)。
文摘Let(X, d, μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderón-Zygmund operator and b:=(b1,..., bm) be a finite family of RBMO(μ) functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator T∏bgenerated by T and b are obtained.
基金supported by the National Natural Science Foundation of China(No.12071052).
文摘An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss,which is equipped with a measure satisfying an additional reverse doubling property.In this paper we study the boundedness of multilinear singular integral operators in weighted Morrey spaces within the framework of RD-spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.11371096 and 11471113)
文摘A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and only if A and B are unitarily equivalent.We also study the reducing subspaces of A^kI+IB^l and give some examples.As an application,we study the reducing subspaces of multiplication operators Mzk+αωl on function spaces.
基金This research was supported in part by a Foundation from Academy of Sciences of China.
文摘It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥1,where ansatisfiesan=1.In[8],the author obtainedsimilar result for the hyponormal weighted unilateral shift of multiplicity 2.The aim of this
基金supported by National Natural Science Foundation of China (Grant Nos. 11401175, 11501169 and 11471041)the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)+2 种基金Program for New Century Excellent Talents in University (Grant No. NCET-13-0065)Grantin-Aid for Scientific Research (C) (Grant No. 15K04942)Japan Society for the Promotion of Science
文摘Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）dξ1dξ2︱^2dt/t）^1/2.Let s be an integer with s ∈ [n ＋ 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p） and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p（νω） if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 ＋ 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p,∞（νω）. The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before.
基金supported by the National Research Foundation of Korea Grant Funded by the Korea Government (Grant No. NRF-2015R1D1A3A01019789)
文摘We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.
