Variable exponent Herz type Besov and Triebel–Lizorkin spaces

2018 ◽  
Vol 25 (1) ◽  
pp. 135-148 ◽  
Author(s):  
Jingshi Xu ◽  
Xiaodi Yang
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Maximal Functions ◽  
Herz Spaces ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractWe establish the boundedness of the vector-valued Hardy–Littlewood maximal operator in variable exponent Herz spaces, which were introduced by Samko in [33]. We also introduce variable exponent Herz type Besov and Triebel–Lizorkin spaces and give characterizations of these new spaces by maximal functions.

scholarly journals New Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Baohua Dong ◽  
Jingshi Xu
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Vector Valued ◽  
Littlewood Maximal Operator

The authors establish the boundedness of vector-valued Hardy-Littlewood maximal operator in Herz spaces with variable exponents. Then new Herz type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Finally, characterizations of these new spaces by maximal functions are given.

Endpoint Regularity of Multisublinear Fractional Maximal Functions

2017 ◽  
Vol 60 (3) ◽  
pp. 586-603 ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Maximal Operators ◽  
One Dimensional ◽  
Regularity Properties ◽  
The One ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractIn this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy–Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on the vector-valued function with all ƒ j being BV-functions.

scholarly journals Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Joaquín Motos ◽  
María Jesús Planells ◽  
César F. Talavera
Keyword(s):  
Analytic Functions ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Previous Article ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Complemented Subspace ◽  
Open Set ◽  
Hörmander Spaces ◽  
Littlewood Maximal Operator

We show that the dual Bp·locΩ′ of the variable exponent Hörmander space Bp(·)loc(Ω) is isomorphic to the Hörmander space B∞c(Ω) (when the exponent p(·) satisfies the conditions 0<p-≤p+≤1, the Hardy-Littlewood maximal operator M is bounded on Lp(·)/p0 for some 0<p0<p- and Ω is an open set in Rn) and that the Fréchet envelope of Bp(·)loc(Ω) is the space B1loc(Ω). Our proofs rely heavily on the properties of the Banach envelopes of the p0-Banach local spaces of Bp(·)loc(Ω) and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for p(·)≡p, 0<p<1, are also given (e.g., all quasi-Banach subspace of Bploc(Ω) is isomorphic to a subspace of lp, or l∞ is not isomorphic to a complemented subspace of the Shapiro space hp-). Finally, some questions are proposed.

scholarly journals A Weak Type Vector-Valued Inequality for the Modified Hardy–Littlewood Maximal Operator for General Radon Measure on ℝn

2020 ◽  
Vol 8 (1) ◽  
pp. 261-267
Author(s):  
Yoshihiro Sawano
Keyword(s):  
Radon Measure ◽  
Maximal Operator ◽  
Weak Type ◽  
Strong Type ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractThe aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy– Littlewood maximal operator for general Radon measure on ℝn. Earlier, the strong type vector-valued inequality for the same operator and the weak type vector-valued inequality for the dyadic maximal operator were obtained. This paper will supplement these existing results by proving a weak type counterpart.

A note on the behavior of the Dunkl maximal operator

2018 ◽  
Vol 9 (4) ◽  
pp. 237-246 ◽  
Author(s):  
Luc Deleaval
Keyword(s):  
Maximal Operator ◽  
Mathematical Society ◽  
Vector Valued ◽  
Littlewood Maximal Operator

Abstract This note is a contribution to the Proceedings of the Conference of the Tunisian Mathematical Society CSMT 2017. After briefly revisiting the case of the standard Hardy–Littlewood maximal operator, we will discuss the behavior of the Dunkl maximal operator in both the scalar and vector-valued cases.

An Almost Greedy Uniformly Bounded Orthonormal Basis in 𝐿𝑝(·)([0, 1]) Spaces

2009 ◽  
Vol 16 (3) ◽  
pp. 465-474
Author(s):  
Ana Danelia ◽  
Ekaterine Kapanadze
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Orthonormal Basis ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Greedy Basis ◽  
Littlewood Maximal Operator ◽  
Uniformly Bounded

Abstract We construct a uniformly bounded orthonormal almost greedy basis for the variable exponent Lebesgue spaces 𝐿𝑝(·)([0, 1]), 1 < 𝑝– ≤ 𝑝+ ≤ 2 (or 2 ≤ 𝑝– ≤ 𝑝+ < ∞), when the diadic Hardy–Littlewood maximal operator is bounded on these spaces.

Sign in / Sign up

Export Citation Format

Share Document