Index modulation aided generalized space-time block coding:A unified MIMO framework

In this paper,Index Modulation(IM)aided Generalized Space-Time Block Coding(GSTBC)is proposed,which intrinsically exploits the benefits of IM concept,diversity gain and spatial multiplexing gain.Specifically,the information bits are partitioned into U groups,with each being modulated by IM symbols(i.e.Spatial Modulation(SM),Quadrature SM(QSM),etc).Next,the structure of GSTBC is invoked for each K IM symbol,and a total ofμ=U/K GSTBC codes are transmitted via T time slots.A Block Expectation Propagation(B-EP)detector is designed for the proposed IM-GSTBC structure.Moreover,the theoretical Average Bit Error Probability(ABEP)is derived for our IM-GSTBC system,which is confirmed by the simulation results and helpful for performance evaluation.Simulation results show that our proposed IM-GSTBC system is capable of striking an efficient trade-off between spatial multiplexing gain,spatial diversity gain as well as implementation cost imposed for both small-scale and large-scale MIMO antenna configurations.

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).

QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.

QUASI_EQUILIBRIUM PROBLEMS IN NONCOMPACT GENERALIZED CONVEX SPACES

By applying a new fixed point theorem due to the author, some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces. These theorems improve and generalize a number of important known results in recent literature.

Boundedness of multilinear operators on generalized Morrey spaces

In this paper, the authors prove the boundedness of the multilinear maximal func- tions, multilinear singular integrals and multilinear Riesz potential on the product generalized Rn Rn Morrey spaces Mp1,ωw1 （Rn）×…×Mpm,ω （Rn） respectively. The main theorems of this paper extend some known results.

TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.

MULTILINEAR CALDERóN-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.

μ-Separations in generalized topological spaces

This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.

Fan-Browder Type Fixed Point Theorems and Its Applications on Generalized Convex Product Spaces

Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of（partially） maximai element and equilibrium point are discussed as applications of above results.

CARLESON MEASURES AND THE GENERALIZED CAMPANATO SPACES OF VECTOR-VALUED MARTINGALES

In this paper, the so-called（p,Ф）-Carleson measure is introduced and the rela-tionship between vector-valued martingales in the general Campanato spaces Lp,Ф（X） and the （p, Ф）-Carleson measures is investigated. Specifically, it is proved that for q ∈ [2, ∞）, the measure d# ：-=││ dfk││^qdP dm is a （q, Ф）-Carleson measure on Ω × N for every f ∈ Lq,Ф（X） if and only if X has an equivalent norm which is q-uniformly convex; while for p C （1, 2], the measure dμ ：=││dfk││^pP dm is a （p, Ф）-Carleson measure on Ω ×N implies that f ∈ Lp,Ф（X） if and only if X admits an equivalent norm which is p-uniformly smooth. This result extends an earlier result in the literature from BMO spaces to general Campanato spaces.

Boundedness for Maximal Bochner-Riesz Operator and Commutator on Generalized Morrey Space

In this paper,we have obtained the boundedness of maximal Bochner-Riesz operator on generalized Morrey space.Also,it is right for its commutator.

BOUNDEDNESS FOR THE COMMUTATOR OF FRACTIONAL INTEGRAL ON GENERALIZED MORREY SPACE IN NONHOMOGENEOUS SPACE

In this paper, we will establish the boundedness of the commutator generated by fractional integral operator and RBMO（μ） function on generalized Morrey space in the non-homogeneous space.

NONCOMPACT INFINITE OPTIMIZATION AND EQUILIBRIA OF CONSTRAINED GAMES IN GENERALIZED CONVEX SPACES

By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure. These theorems improve and generalize a number of important results in recent literature.

LITTLEWOOD-PALEY OPERATORS AND MARCINKIEWICZ INTEGRAL ON GENERALIZED CAMPANATO SPACES

Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.

Schmidt Decomposition of Quaternion Matrix and the Orthonormalization of Vectors in a Generalized Unitary Space

In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.

A Generalized State Space Average Model for Parallel DC-to-DC Converters

The high potentiality of integrating renewable energies,such as photovoltaic,into a modern electrical microgrid system,using DC-to-DC converters,raises some issues associated with controller loop design and system stability.The generalized state space average model(GSSAM)concept was consequently introduced to design a DC-to-DC converter controller in order to evaluate DC-to-DC converter performance and to conduct stability studies.This paper presents a GSSAM for parallel DC-to-DC converters,namely:buck,boost,and buck-boost converters.The rationale of this study is that modern electrical systems,such as DC networks,hybrid microgrids,and electric ships,are formed by parallel DC-to-DC converters with separate DC input sources.Therefore,this paper proposes a GSSAM for any number of parallel DC-to-DC converters.The proposed GSSAM is validated and investigated in a time-domain simulation environment,namely a MATLAB/SIMULINK.The study compares the steady-state,transient,and oscillatory performance of the state-space average model with a fully detailed switching model.

Korn's Inequality and Divergence Equations on Generalize Orlicz Spaces

Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.