Luong Dang Ky
Bilinear decompositions and commutators of singular integral operators.
Wed, 05/04/2011 - 15:01 — SomNambulAuthors: Luong Dang Ky
Subjects: Classical Analysis and ODEs
AbstractLet $b$ be a $BMO$-function. It is well-known that the linear commutator $[b,
T]$ of a Calder\'on-Zygmund operator $T$ does not, in general, map continuously
$H^1(\mathbb R^n)$ into $L^1(\mathbb R^n)$. However, P\'erez \cite{Pe} showed
that if $H^1(\mathbb R^n)$ is replaced by a suitable atomic subspace $\mathcal
H^1_b(\mathbb R^n)$ then the commutator is continuous from $\mathcal
H^1_b(\mathbb R^n)$ into $L^1(\mathbb R^n)$.New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators.
Tue, 03/22/2011 - 16:01 — SomNambulAuthors: Luong Dang Ky
Subjects: Classical Analysis and ODEs
AbstractWe introduce a new class of Hardy spaces $H^{\phi(\cdot,\cdot)}(\mathbb
R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the
Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\'ia-Cuerva,
Str\"omberg, and Torchinsky. Here, $\phi: \mathbb R^n\times [0,\infty)\to
[0,\infty)$ is a function such that $\phi(x,\cdot)$ is an Orlicz function and
$\phi(\cdot,t)$ is a Muckenhoupt $A_\infty$ weight. A function $f$ belongs to
$H^{\phi(\cdot,\cdot)}(\mathbb R^n)$ if and only if its maximal function $f^*$
is so that $x\mapsto \phi(x,|f^*(x)|)$ is integrable.
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