Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms write by Alexander Nagel. This book was released on 2019-01-08. Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms available in PDF, EPUB and Kindle. The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.
Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting
Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting write by Yongsheng Han. This book was released on 2022-08-31. Maximal Functions, LittlewoodPaley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting available in PDF, EPUB and Kindle. View the abstract.
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Mercer Kernels and Reproducing Kernel Banach Spaces write by Yuesheng Xu. This book was released on 2019-04-10. Generalized Mercer Kernels and Reproducing Kernel Banach Spaces available in PDF, EPUB and Kindle. This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .
Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance
Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance write by Jun Kigami. This book was released on 2019-06-10. Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance available in PDF, EPUB and Kindle. In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.
Spinors on Singular Spaces and the Topology of Causal Fermion Systems
Spinors on Singular Spaces and the Topology of Causal Fermion Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spinors on Singular Spaces and the Topology of Causal Fermion Systems write by Felix Finster. This book was released on 2019-06-10. Spinors on Singular Spaces and the Topology of Causal Fermion Systems available in PDF, EPUB and Kindle. Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.
