Results 91 to 100 of about 7,070 (191)

Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces

Abstract and Applied Analysis, 2016
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 ...
Joaquín Motos, María Jesús Planells, César F. Talavera   +2 more
doaj   +1 more source

Modified Hardy-Littlewood maximal operators on nondoubling metric measure spaces

Annales Academiae Scientiarum Fennicae Mathematica, 2015
Summary: We investigate the modified Hardy-Littlewood maximal operators, uncentered \[ M_k f(x) = \sup \frac{1}{\mu(kB)} \int_B |f|\,d\mu, \] and centered \[ M_k^c f(x) = \sup \frac{1}{\mu(B(x,kr)} \int_{B(x,r)} |f|\,d\mu,\quad k\geq 1, \] in the setting of a general measure space \((X,d\mu)\). By using an enhanced version of the basic covering theorem
openaire   +2 more sources

Lower Bounds and Fixed Points for the Centered Hardy–Littlewood Maximal Operator [PDF]

The Journal of Geometric Analysis, 2019
For all $p>1$ and all centrally symmetric convex bodies $K\subset \mathbb{R}^d$ define $Mf$ as the centered maximal function associated to $K$. We show that when $d=1$ or $d=2$, we have $||Mf||_p\ge (1+ (p,K))||f||_p$. For $d\ge 3$, let $q_0(K)$ be the infimum value of $p$ for which $M$ has a fixed point.
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Bessel–Riesz Operator in Variable Lebesgue Spaces L^p(·)(${\mathbb{R}}_{+}$)

Axioms
This paper investigates the Bessel–Riesz operator within the framework of variable Lebesgue spaces. We extend existing results by establishing boundedness under more general conditions.
Muhammad Nasir, Fehaid Salem Alshammari, Ali Raza   +2 more
doaj   +1 more source

On the sharpness of some quantitative Muckenhoupt–Wheeden inequalities

Comptes Rendus. Mathématique
In the recent work [Cruz-Uribe et al. (2021)] it was obtained that \[ |\lbrace x\in {\mathbb{R}^d}:w(x)|G(fw^{-1})(x)|>\alpha \rbrace |\lesssim \frac{[w]_{A_1}^2}{\alpha }\int _{{\mathbb{R}^d}}|f|\,\mathrm{d} x \] both in the matrix and scalar settings ...
Lerner, Andrei K., Li, Kangwei, Ombrosi, Sheldy, Rivera-Ríos, Israel P.   +3 more
doaj   +1 more source

Boundedness of maximal functions on non-doubling manifolds with ends

, 2013
Let $M$ be a manifold with ends constructed in \cite{GS} and $\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal function ...
Duong, Xuan Thinh, Li, Ji, Sikora, Adam
core  

Maximal function and generalized fractional integral operators on the weighted Orlicz-Lorentz-Morrey spaces

Open Mathematics
We define the weighted Orlicz-Lorentz-Morrey and weak weighted Orlicz-Lorentz-Morrey spaces to generalize the Orlicz spaces, the weighted Lorentz spaces, the Orlicz-Lorentz spaces, and the Orlicz-Morrey spaces.
Li Hongliang
doaj   +1 more source

A new Bihari inequality and initial value problems of first order fractional differential equations. [PDF]

Fract Calc Appl Anal, 2023
Lan K, Webb JRL.
europepmc   +1 more source

Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions

Discrete Analysis, 2018
Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions, Discrete Analysis 2018:10, 18pp. An important role in harmonic analysis is played by the notion of a _maximal function_ (which is actually a non-linear operator on a space of ...
Theresa C. Anderson, Brian Cook, Kevin Hughes, Angel Kumchev   +3 more
doaj   +1 more source

Weighted Lorentz Spaces, Variable Exponent Analysis, and Operator Extensions

Axioms
We develop novel extensions in the theory of weighted Lorentz spaces. In particular, we generalize classical results by introducing variable-exponent Lorentz spaces, establish sharp constants and quantitative bounds for maximal operators, and extend the ...
Saeed Hashemi Sababe, Ismail Nikoufar
doaj   +1 more source