BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS SPACES

For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

Riesz potentials of Hardy-Hausdorff spaces and Q-type spaces

This study investigates the restriction problem for the Riesz potentials of Hardy-Hausdorff spaces HH^1-γ(R^n)and Q-type spaces Qγ(R^n).By exploiting a geometric-measure theory generated by the indicatorlike functions of compact sets,it is proved that the Riesz operator Iαcontinuously maps HH^1-γ(R^n)into the weak Morrey spaces L^q,λ/μ,*induced by a Radon measureμ,which obeys a geometric condition.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Some properties of Riesz potential associated with Schrdinger operator

Let L = --△ ＋ Ⅴ be the SchrSdinger operator on Rd, d ≥ 3, where A is the Laplacian on Rd and V ≠ 0 is a nonnegative function satisfying the reverse HSlder inequality. In this article, the author investigates some properties of the Riesz potential IaL associated with L on the Campanato-type spaces ∧Lβ and the Hardy-type spaces HLP.

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.

Bessel (Riesz) Potentials on Banach Function Spaces and Their Applications I Theory

In this paper, we shall introduce the concept of the Bessel （Riesz） potential Kothe function spaces Xs （s） and give some dual estimates for a class of operators determined by a semi-group in the spaces Lq （-T, T; Xs） （Lq（-T, T; s ））. Moreover, some time-space LP-LP estimates for the semi-group exp(it（-△）m/2) and the operator A:=∫0t exp(i（t-τ）（-△）m/2). dτ in the Lebesgue-Besov spaces Lq(-T, T; p,2S) are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.

ON THE HEAT KERNEL OF THE RIEMANNIAN SYMMETRIC SPACE SU(6)/SP(3)

By using the Hba's expression of the inverse Abel transform for the Riemannian symmetric space SU* (6)/SP(3) , we obtain the analytic expression of the heat kernal e(t Delta) for this space, and then deduce the weak (1-1) boundedness of the maximal operator associated to the heat kernel, we obtain also the asymptotic behavious of the Riesz potential (Delta)(-1/2) near infinite and near the origin. Finally we study the integrability of the Riesz transform Brad (Delta)(-1/2).

L_2-Optimal Recovery on the Riesz Potential Spaces

The problems of best reconstruction of multivariate functions of the Riesz potential spaces from their values on a given mesh are considered, and the exact results of some classes of L_2(R^n) (and L_2(Q^n)) defined by the Riesz potential are obtained.

On Gauss-Weierstrass Semigroups and Inversion of Potentials Associated with the Bessel Differential Operator

In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.

Commutator of Riesz potential in p-adic generalized Morrey spaces

Suppose that Ip^α is the p-adic Riesz potential. In this paper, we established the boundedness of Ip^α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential Ip^α and p-adic generalized Campanato functions. Keywords

Trigonometric multiplicative chaos and applications to random distributions

The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.

Generalized Hardy Spaces

Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.

THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.

AVERAGE σ-K WIDTH OF CLASS OF L_p(R^n) IN L_q (R^n)

The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.

REMARKS ON THE EXISTENCE OF WEAK SOLUTIONS TO 2-D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.