共查询到20条相似文献,搜索用时 0 毫秒
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We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results. 相似文献
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In this paper, we study the approximation of identity operator and the convolution integral operator Bm by Fourier partial sum operators, Fejr operators, Valle-Poussin operators, Cesárooperators and Abel mean operators, respectively, on the periodic Wiener space (C1(R),Wo) and obtainthe average error estimations. 相似文献
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In this paper we extend the DiPerna-Lions theory of flows associated to Sobolev vector fields to the case of Cameron-Martin-valued vector fields in Wiener spaces E having a Sobolev regularity. The proof is based on the analysis of the continuity equation in E, and on uniform (Gaussian) commutator estimates in finite-dimensional spaces. 相似文献
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Miloud Assal 《数学学报(英文版)》2009,25(9):1543-1560
In this paper we introduce the homogeneous Besov type spaces ∧p,q^γ(K) on the dual of Laguerre hypergroup K and we establish some new harmonic analysis results. We give some character- izations of these spaces using equivalent seminorms. Also we study the non-homogeneous Besov type spaces ∧p,q^γ(K). We give some properties of these spaces and embeddings results with respect to their parameters p, q and γ. 相似文献
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Alireza Ranjbar-Motlagh 《Journal of Mathematical Analysis and Applications》2022,505(2):125508
The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces. 相似文献
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The boundedness of the finite Hilbert transform operator on certain weighted Lp spaces is well known. We extend this result to give the boundedness of that operator on certain weighted Sobolev spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this paper, we study the boundedness of the Schrödinger propagator on Wiener amalgam spaces. In particular, we determine the necessary and sufficient conditions for the propagator to be bounded from to . 相似文献
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Elena Cordero 《Journal of Functional Analysis》2008,254(2):506-534
We study the action of metaplectic operators on Wiener amalgam spaces, giving upper bounds for their norms. As an application, we obtain new fixed-time estimates in these spaces for Schrödinger equations with general quadratic Hamiltonians and Strichartz estimates for the Schrödinger equation with potentials V(x)=±2|x|. 相似文献
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The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B_n in C~n. 相似文献
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We study embeddings of spaces of Besov-Morrey type, M Bp1,q1s1,r1(Rd ) → M Bp2 ,q2s2 ,r2 (R d ), and obtain necessary and sufficient conditions for this. Moreover, we can also characterise the special weighted situation Bp1 ,r1s1 (R d , w) → M Bp2 ,q2s2 ,r2 (Rd ) for a Muckenhoupt A ∞ weight w, with wα(x) = |x|α , α -d1, as a typical example. 相似文献
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Mitsuru Sugimoto 《Journal of Functional Analysis》2007,248(1):79-106
We consider the dilation property of the modulation spaces Mp,q. Let be the dilation operator, and we consider the behavior of the operator norm ‖Dλ‖Mp,q→Mp,q with respect to λ. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov spaces, which was proved by Toft [J. Toft, Continuity properties for modulation spaces, with applications to pseudo-differential calculus, I, J. Funct. Anal. 207 (2004) 399-429]. 相似文献
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The wavelet transform is defined for Wiener functionals. We characterize global and local regularities of Wiener functionals and we give a criterion for the existence and regularity of densities. Such a criterion is applied to diffusion processes and to the solutions to backward stochastic differential equations. 相似文献
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S. Thangavelu 《Journal of Functional Analysis》2007,251(2):438-462
Using Gutzmer's formula, due to Lassalle, we characterise the images of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces. We also obtain necessary and sufficient conditions on a holomorphic function to be in the image of smooth functions and distributions under the Segal-Bargmann transform. 相似文献
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We prove new optimal bounds for the error of numerical integration in bivariate Besov spaces with dominating mixed order r. The results essentially improve on the so far best known upper bound achieved by using cubature formulas taking points from a sparse grid. Motivated by Hinrichs’ observation that Hammersley type point sets provide optimal discrepancy estimates in Besov spaces with mixed smoothness on the unit square, we directly study quasi-Monte Carlo integration on such point sets. As the main tool we prove the representation of a bivariate periodic function in a piecewise linear tensor Faber basis. This allows for optimal worst case estimates of the QMC integration error with respect to Besov spaces with dominating mixed smoothness up to order r<2. The results in this paper are the first step towards sharp results for spaces with arbitrarily large mixed order on the d-dimensional unit cube. In fact, in contrast to Fibonacci lattice rules, which are also practicable in this context, the QMC methods used in this paper have a proper counterpart in d dimensions. 相似文献
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Michael Ruzhansky Mitsuru Sugimoto Joachim Toft Naohito Tomita 《Mathematische Nachrichten》2011,284(16):2078-2092
In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling–Helson type theorems. We also establish a number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on ${\mathscr F}L^q$. Finally, counterparts of these results are discussed for spaces on the torus. 相似文献
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The relationship of Besov spaces and Herz spaces on local fields is given. As an application, one multiplier theorem is obtained.
And the decompositional characterization of the weighted Besov spaces is established. 相似文献
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We consider the problem of reconstruction of functions f from generalized Paley–Wiener spaces in terms of their values on complete interpolating sequence {zn}. We characterize the set of data sequences {f(zn)} and exhibit an explicit solution to the problem. Our development involves the solution of a particular problem. 相似文献
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Robert Fernholz 《Journal of multivariate analysis》1977,7(4):602-607
Measurable linear transformations from an abstract Wiener space to a Hilbert space are characterized. It is shown that the measure on any infinite dimensional abstract Wiener space can be transformed to that on any other by a measurable linear transformation. 相似文献