Semiclassical propagator and van Vleck in a mixed position-momentum determinant space

In this paper a semiclassical propagator in a mixed position-momentum space is derived in the formalism of Maslov＇s multi-dimensional semiclassical theory. The corresponding mixed van Vleck determinant is also given explicitly. The propagator can be used to locally fix semiclassical divergences in singular regions of configuration space. It is shown that when a semicla^sical propagator is transformed from one representation to another, its form is invariant.

MIXED HARDY SPACES AND THEIR APPLICATIONS

Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

The purpose of this paper is to introduce bi-parameter mixed Lipschitz spaces and characterize them via the Littlewood-Paley theory.As an application,we derive a boundedness criterion for singular integral operators in a mixed Journéclass on mixed Lipschitz spaces.Key elements of the paper are the development of the Littlewood-Paley theory for a special mixed Besov spaces,and a density argument for the mixed Lipschitz spaces in the weak sense.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF R^n

Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along"polynomial curves".Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness,the authors prove that such operators are bounded on the mixed radial-angular spaces.Meanwhile,corresponding vector-valued versions are also obtained.

BERGMAN TYPE OPERATOR ON MIXED NORM SPACES WITH APPLICATIONS

The authors investigate the conditions for the boundedness of Bergman type operators Ps,t in mixed norm space L_(p),q(φ)on the unit ball of C^(n)(n≥1),and obtain a sufficient condition and a necessary condition for general normal functionφ,and a sufficient and necessary condition forφ(r)=(1-r 2)αlogβ(2(1-r)-1)(α>0,β≥0).This generalizes the result of Forelli Rudin on Bergman operator in Bergman space.As applications,a more natural method is given to compute the duality of the mixed norm space,solve the Gleason's problem for mixed norm space and obtain the characterization of mixed norm space in terms of partial derivatives.Moreover,it is proved thatf∈L(0)∞,q(φ)iff all the functions(1-|z|2)|α||α|fzα(z)∈L(0)∞,q(φ)for holomorphic functionf,1≤q≤∞.

Coefficient multipliers of mixed norm space in the ball Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤u≤∞, 1≤u, q≤∞. (iii) 1≤v≤2≤q≤∞, and 0<p≤u≤∞or 1≤p, u≤∞. The first case extends the result of Blasco, Jevtic, and Pavlovic in one variable. The third case generalizes partly the results of Jevtic, Jovanovic, and Wojtaszczyk to higher dimensions.

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).

The Lp,q-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces Lp,q(Rd+1)

The stability is an expected property for functions, which is widely considered in the study of approximation theory and wavelet analysis. In this paper, we consider the L^p,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1）. We first show that the shifts Φ（·- k） （k∈Z^d＋1） are L^p,q-stable if and only if for any ξ ∈R^d＋1,∑κ∈Z^d＋1 ]｜Φ^^（ξ ＋ 2πκ）]^2 〉 0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1） to be L^p,q-stable which improves some known results.

Carleson Type Measures for Harmonic Mixed Norm Spaces with Application to Toeplitz Operators

Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.

Compact Ceshro Operators from Spaces H（p,q,u） to H（p, q, v）

Let μ and v be normal functions and let Tg be the extended Ceshso operator in terms of the symbol g. In this paper, we will characterize those g so that Tg is bounded （or compact） from mixed norm spaces H（p, q, μ） to H（p, q, v） in the unit ball of C^n, Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces.

Reduction of FWM noise in WDM-based QKD systems using interleaved and unequally spaced channels

To extensively deploy quantum key distribution（QKD） systems, copropagating with classical channels on the same fiber using wavelength division multiplexing（WDM） technology becomes a critical issue. We propose a user-based channel-interleaving WDM scheme with unequal frequency spacing（UFS-i WDM） to reduce the impairment on the quantum channels induced by four-wave mixing（FWM）, and theoretically analyze its impact on quantum bit error rate（QBER）. Numerical simulation results show that a UFS-i WDM can significantly reduce the FWM noise and improve QBER compared with the corresponding WDM scheme with equal frequency spacing（EFS）, especially in the case of nonzero dispersion shifted fiber.

Parabolic Littlewood-Paley g-Function with Rough Kernel

In this note, we give the L^p （1 〈 p 〈∞） boundedness of the parabolic Littlewood Paley g-function with rough kernel.

The information-based complexity of approximation problem by adaptive Monte Carlo methods

In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.

Fractional beamforming of dense spacing array for time-frequency mix

The model of time-frequency mixed processing and the towing experimental results airs discussed in the paper for the fractional beamforming of a dense spacing array. The results show that the theoretical model is in agreement with the experimental results and it can.be realized easily in the engineering mode. The Performance Figure of the experimental subarray system is increased about 17 dB in comparison with that of traditional array with halfwavelength spacing between elements under the same conditions, when the flow noise is a dominant component in the background noise received by a sub-array.