Isomorphisms and several characterizations of Musielak-Orlicz-Hardy spaces associated with some Schrödinger operators

Title:

Isomorphisms and several characterizations of Musielak-Orlicz-Hardy spaces associated with some Schrödinger operators

Creator:

Yang, Sibei

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ebed77f6-e37f-4276-8c8a-c77bd209641e
uuid:ebed77f6-e37f-4276-8c8a-c77bd209641e
issn:0011-4642

Subject:

mathematics, Musielak-Orlicz-Hardy space, Schrödinger operator, L-harmonic function, isomorphism of Hardy space, atom, molecule, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let L := −Δ + V be a Schrödinger operator on\mathbb{R}^{n} with n\geqslant 3 and V\geqslant 0 satisfying \Delta ^{-1}V\in L^{\infty }(\mathbb{R}^{n}). Assume that φ: {R}^{n} × [0,∞) → [0,∞) is a function such that φ(x,,) is an Orlicz function, φ(•, t) \in A_{\infty }({R}^{n}) (the class of uniformly Muckenhoupt weights). Let w be an L-harmonic function on {R}^{n} with 0< C_{1}\leq w\leq C_{2}, where C_{1} and C_{2} are positive constants. In this article, the author proves that the mapping H_{\phi ,L} (\mathbb{R}^n ) \mathrel\backepsilon f \mapsto wf \in H_\phi (\mathbb{R}^n ) is an isomorphism from the Musielak-Orlicz-Hardy space associated with L,H_{\phi ,L} (\mathbb{R}^n ), to the Musielak-Orlicz-Hardy space H_\phi (\mathbb{R}^n ) under some assumptions on φ. As applications, the author further obtains the atomic and molecular characterizations of the space H_{\phi ,L} (\mathbb{R}^n ) associated with w, and proves that the operator {( - \Delta )^{ - 1/2}}{L^{1/2}} is an isomorphism of the spaces H_{\phi ,L} (\mathbb{R}^n ) and H_\phi (\mathbb{R}^n ). All these results are new even when φ(x, t) ≔ t^{p}, for all x \in \mathbb{R}^{n} and t \in [0,∞), with p ∞ (n/(n + μ_{0}), 1) and some μ_{0} \in (0, 1]., Sibei Yang., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

747-779

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:3

Harvested from:

CDK

Metadata only:

false