Function spaces via fractional Poisson kernel on Carnot groups and applications
نویسندگان
چکیده
We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel Poisson kernel. apply our results to study commutators involving powers sub-Laplacian.
منابع مشابه
compactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولImplicit Function Theorem in Carnot–carathéodory Spaces
In this paper, we study the notion of regular surface in the Carnot–Carathéodory spaces and we prove the implicit function theorem in this setting. We fix at every point of R a subset of the tangent space, called horizontal tangent plane, and we assume that it has a basis X1, . . . , Xm of C∞ vector fields satisfying the Hörmander condition of hypoellipticity, (see [16]). This choice induces a ...
متن کاملConvex Functions on Carnot Groups
We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
متن کاملCompensated Compactness for Differential Forms in Carnot Groups and Applications
In this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a Carnot group. The proof relies on a L–Hodge decomposition for these forms. Because of the lack of homogeneity of the intrinsic exterior differential, Hodge decomposition is proved using the parametrix of a suitable 0order Laplacian on forms.
متن کاملFractional Poisson Process
For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal D Analyse Mathematique
سال: 2023
ISSN: ['0021-7670', '1565-8538']
DOI: https://doi.org/10.1007/s11854-022-0255-y