scholarly journals Herz type Hardy spaces on non-homogeneous metric measure space

2018 ◽  
Vol 48 (10) ◽  
pp. 1315
Author(s):  
Han Yaoyao ◽  
Zhao Kai
2014 ◽  
Vol 91 (2) ◽  
pp. 286-302
Author(s):  
GUORONG HU

AbstractLet $(X,d,{\it\mu})$ be a metric measure space satisfying the doubling, reverse doubling and noncollapsing conditions. Let $\mathscr{L}$ be a nonnegative self-adjoint operator on $L^{2}(X,d{\it\mu})$ satisfying a pointwise Gaussian upper bound estimate and Hölder continuity for its heat kernel. In this paper, we introduce the Hardy spaces $H_{\mathscr{L}}^{p}(X)$, $0<p\leq 1$, associated to $\mathscr{L}$ in terms of grand maximal functions and show that these spaces are equivalently characterised by radial and nontangential maximal functions.


2017 ◽  
Vol 2017-3 (103) ◽  
pp. 19-28
Author(s):  
Luigi Ambrosio ◽  
Nicola Gigli ◽  
Giuseppe Savaré

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Toni Heikkinen

Let Φ be anN-function. We show that a functionu∈LΦ(ℝn)belongs to the Orlicz-Sobolev spaceW1,Φ(ℝn)if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.


2010 ◽  
Vol 106 (2) ◽  
pp. 283 ◽  
Author(s):  
Oscar Blasco ◽  
Vicente Casanova ◽  
Joaquín Motos

Given a metric measure space $(X,d,\mu)$, a weight $w$ defined on $(0,\infty)$ and a kernel $k_w(x,y)$ satisfying the standard fractional integral type estimates, we study the boundedness of the operators $K_w f(x)=\int_X k_w(x,y)f(y)\,d\mu(y)$ and $\tilde K_w f(x)=\int_X (k_w(x,y)-k_w(x_0,y))f(y)\,d\mu(y)$ on Lebesgue spaces $L^p(\mu)$ and generalized Lipschitz spaces $\mathrm{Lip}_\phi$, respectively, for certain range of the parameters depending on the $n$-dimension of $\mu$ and some indices associated to the weight $w$.


2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Marcello Lucia ◽  
Michael J. Puls

Abstract Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.


2016 ◽  
Vol 48 (10) ◽  
Author(s):  
Nafiseh Rahmanpour ◽  
Hossein Shojaie

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