Sharp asymptotic estimates for a class of Littlewood–Paley operators
نویسندگان
چکیده
It is well-known that Littlewood–Paley operators formed with respect to lacunary sets of finite order are bounded on $L^p (\mathbb {R})$ for all $1 \lt p \infty $. In this note it shown $$ \| S_{\mathcal {I}_{E_2}} \|_{L^p {R}) \right
منابع مشابه
Sharp Lorentz Space Estimates for Rough Operators
We demonstrate the (H, L) or (L, L) mapping properties of several rough operators. In all cases these estimates are sharp in the sense that the Lorentz exponent 2 cannot be replaced by any lower number.
متن کاملSharp Boundary Estimates for Elliptic Operators
L 2 boundary decay properties of the heat kernel and spectral density. We deduce bounds on the rate of convergence of the eigenvalues when the region is slightly reduced in size. It is remarkable that several of the bounds do not involve the space dimension. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: boundary decay, Laplacian, Hardy inequality, eigenfunctions, heat kernel...
متن کاملSome Sharp Weighted Estimates for Multilinear Operators
In[6], Hu and Yang obtain a variant sharp estimate for the multilinear singular integral operators. The main purpose of this paper is to prove a sharp inequality for some multilinear operators related to certain non-convolution type integral operators. In fact, we shall establish the sharp inequality for the multilinear operators only under certain conditions on the size of the integral operato...
متن کاملSharp Weyl Estimates for Tensor Products of Pseudodifferential Operators
We study the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on R, respectively. We obtain, in particular, the sharpness of the remainder term in the corresponding Weyl formulae, which we prove by means of the analysis of some e...
متن کاملSharp Estimates for Maximal Operators Associated to the Wave Equation
The wave equation, ∂ttu = ∆u, in R, considered with initial data u(x, 0) = f ∈ H(R) and u′(x, 0) = 0, has a solution which we denote by 1 2 (e √ −∆f + e−it √ −∆f). We give almost sharp conditions under which sup0<t<1 |e ±it √ −∆f | and supt∈R |e ±it √ −∆f | are bounded from H(R) to L(R).
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: Studia Mathematica
سال: 2021
ISSN: ['0039-3223', '1730-6337']
DOI: https://doi.org/10.4064/sm200514-6-10