Analysis Mathematica最新文献

In this paper, we extend tools developed in [9] to study Euler T-type sums involving odd harmonic numbers and binomial coefficients. In particular, we will prove that two kinds of Euler T-type sums can be expressed in terms of log(2), zeta values, double T-values, (odd) harmonic numbers and double T-sums.

In this article, some necessary and sufficient conditions areshown for weighted weak type mixed (Phi)-inequality and weighted extra-weak typemixed (Phi)-inequality for martingale maximal operator. The obtained results generalizesome existing statements.

Let (C,Dsubset mathbb{N}) be disjoint sets, and (mathcal{C}={1/2^{c}colon cin C}, mathcal{D}={1/2^{d}colon din D}). We consider the associate bases of dyadic, axis-parallel rectangles (mathcal{R}_{mathcal{C}}) and (mathcal{R}_{mathcal{D}}). We give necessary and sufficient conditions on the sets (mathcal{C} and mathcal{D}) such that there is a positive function (fin L^{1}([0,1)^{2})) so that the integral averages are convergent with respect to (mathcal{R}_{mathcal{C}}) and divergent for (mathcal{R}_{mathcal{D}}). We next apply our results to the two-dimensional Fourier--Haar series and characterize convergent and divergent sub-indices. The proof is based on some constructions from the theory of low-discrepancy sequences such as the van der Corput sequence and an associated tiling of the unit square.

We study the boundary behavior of the Kobayashi--Fuks metric on the class of h-extendible domains. Here, we derive the nontangential boundary asymptotics of the Kobayashi--Fuks metric and its Riemannian volume element by the help of some maximal domain functions and then using their stability results on h-extendible local models.

In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, (h_b), with operator-valued symbols b, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball (mathbb{B}_n).More precisely, given two complex Banach spaces X, Y, we characterize those operator-valued symbols(b colon mathbb{B}_nrightarrow mathcal{L} (overline{X},Y) ) for which the little Hankel operator (h_{b}: A^{Phi_{1}}_{alpha}(mathbb{B}_{n},X) longrightarrow A^{Phi_{2}}_{alpha}(mathbb{B}_{n},Y)), extends into a bounded operator, where (Phi_{1}) and (Phi_2) are either convex or concave growth functions.

We characterize scaling functions of nonstationary matrix-valuedmultiresolution analysis in the matrix-valued function space (L^2(mathbb{R}, mathbb{C}^{l times l})), l is a naturalnumber. This is inspired by the work of Novikov, Protasov and Skopina onnonstationary multiresolution analysis of the space (L^2(mathbb{R})). Using a sequence of diagonalmatrix-valued scaling functions in (L^2(mathbb{R}, mathbb{C}^{l times l})), the construction of matrixvaluednonstationary orthonormal wavelets associated with the affine group ispresented. Nonstationary matrix-valued wavelet frames in terms of frames ofclosed subspaces associated with a given nonstationary multiresolution analysisare given. Finally, we give sufficient conditions for the sequence of scaling functionsof nonstationary matrix-valued multiresolution analysis in the frequencydomain.

We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph.

As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-Hölderian mappings between normed spaces, by studying the action of the mappings on K-functionals and between interpolation spaces with logarithm functions. We apply these results to obtain some regularity results on the gradient of the solutions to quasilinear equations of the form

where V is a nonlinear potential and f belongs to non-standard spaces like Lorentz–Zygmund spaces. We show several results; for instance, that the mapping (cal{T}:cal{T}f=nabla u) is locally or globally α-Hölderian under suitable values of α and appropriate hypotheses on V and â.

In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L² spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.