On Boundedness of Maximal Operators Associated with Hypersurfaces
نویسندگان
چکیده
In this paper, we obtain a criterion of boundedness maximal operators associated with smooth hypersurfaces. Also, compute the exact value index such arbitrary convex analytic hypersurfaces in case where Varchenko height hypersurface is greater than two. We for degenerate hypersurfaces, i.e., satisfying assumptions classical Hartman–Nirenberg theorem. The obtained results justify Stein–Iosevich–Sawyer conjecture as well discuss related problems theory oscillatory integrals.
منابع مشابه
boundedness of maximal averages over hypersurfaces in R 3
Our goal is to determine for which p is the maximal operator M bounded on L. Note that by subadditivity of maximal operators of the form (1.1), one can prove L boundedness of the nonlocalized analogue of (1.1) over a compact surface by doing a partition of unity and reducing to (1.1). If L is an invertible linear transformation and ML denotes the maximal operator corresponding to the surface L(...
متن کاملBoundedness of Maximal Operators and Maximal Commutators on Non-homogeneous Spaces
Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the L boundedness of the maximal commutator with RBMO functions
متن کاملBoundedness of Littlewood-Paley Operators Associated with Gauss Measures
Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space X, d, μ ρ, which means that the set X is endowed with a metric d and a locally doubling regular Borel measure μ satisfying doubling and reverse doubling conditions on admissible balls defined via the metric d and certain admissible function ρ. The authors then construct an approximation of the identity...
متن کاملON THE BOUNDEDNESS OF MAXIMAL OPERATORS AND SINGULAR OPERATORS WITH KERNELS IN L(logL)alpha(Sn-1)
متن کامل
A Note on Maximal Operators Associated with Hankel Multipliers
Let m have compact support in (0,∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the Lprad(R )-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by modifying the proof of the characterization...
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 of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06032-2