On the $H^{p}$-$L^{q}$ boundedness of some fractional integral operators

Title:

On the $H^{p}$-$L^{q}$ boundedness of some fractional integral operators

Creator:

Rocha, Pablo and Urciuolo, Marta

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:bbe49b50-e1bd-4035-a425-7ba76eb71137
uuid:bbe49b50-e1bd-4035-a425-7ba76eb71137

Subject:

integral operator and Hardy space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $A_{1},\dots ,A_{m}$ be $n\times n$ real matrices such that for each $1\leq i\leq m,$ $A_{i}$ is invertible and $A_{i}-A_{j}$ is invertible for $i\neq j$. In this paper we study integral operators of the form $$ Tf( x) =\int k_{1}( x-A_{1}y) k_{2}( x-A_{2}y) \dots k_{m}( x-A_{m}y) f( y) {\rm d} y, $$ $k_{i}( y) =\sum _{j\in \mathbb Z}2^{jn/{q_{i}}}\varphi _{i,j}( 2^{j}y) $, $1\leq q_{i}<\infty,$ $1/{q_{1}}+1/{q_{2}}+\dots +1/{q_{m}}=1-r,$ $0\leq r<1,$ and $\varphi _{i,j}$ satisfying suitable regularity conditions. We obtain the boundedness of $T\colon H^{p}( \mathbb {R} ^{n}) \rightarrow L^{q} (\mathbb {R}^{n}) $ for $ 0<p<1/{r}$ and $1/{q}=1/{p}-r.$ We also show that we can not expect the $H^{p}$-$H^{q}$ boundedness of this kind of operators.

Language:

English

Rights:

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

Coverage:

625-635

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:3

Harvested from:

CDK

Metadata only:

false