144 research outputs found
Anisotropic Singular Integrals in Product Spaces
Let for be an expansive dilation, respectively, on and and . Denote by {\mathcal
A}_\infty(\rnm; \vec A) the class of Muckenhoupt weights associated with . The authors introduce a class of anisotropic singular integrals on , whose kernels are adapted to in the sense of
Bownik and have vanishing moments defined via bump functions in the sense of
Stein. Then the authors establish the boundedness of these anisotropic singular
integrals on with and
or on with and . These results are also new
even when .Comment: Sci. China Math., to appea
Local Hardy Spaces of Musielak-Orlicz Type and Their Applications
Let \phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz) be a function such
that is an Orlicz function and (the class of local weights
introduced by V. S. Rychkov). In this paper, the authors introduce a local
Hardy space of Musielak-Orlicz type by the local grand
maximal function, and a local -type space
which is further proved to be the
dual space of . As an application, the authors prove
that the class of pointwise multipliers for the local
-type space ,
characterized by E. Nakai and K. Yabuta, is just the dual of
L^1(\rn)+h_{\Phi_0}(\mathbb{R}^n), where is an increasing function on
satisfying some additional growth conditions and a
Musielak-Orlicz function induced by . Characterizations of
, including the atoms, the local vertical and the local
nontangential maximal functions, are presented. Using the atomic
characterization, the authors prove the existence of finite atomic
decompositions achieving the norm in some dense subspaces of
, from which, the authors further deduce some
criterions for the boundedness on of some sublinear
operators. Finally, the authors show that the local Riesz transforms and some
pseudo-differential operators are bounded on .Comment: Sci. China Math. (to appear
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
Biomarkers of disease differentiation: HCV recurrence versus acute cellular rejection
The wound-healing process induced by chronic hepatitis C virus (HCV) infection triggers liver damage characterized by fibrosis development and finally cirrhosis. Liver Transplantation (LT) is the optimal surgical treatment for HCV-cirrhotic patients at end-stage liver disease. However, acute cellular rejection (ACR) and HCV recurrence disease represent two devastating complications post-LT. The accurate differential diagnosis between both conditions is critical for treatment choice, and similar histological features represent a challenge for pathologists. Moreover, the HCV recurrence disease severity is highly variable post-LT. HCV recurrence disease progression is characterized by an accelerated fibrogenesis process, and almost 30% of those patients develop cirrhosis at 5-years of follow-up. Whole-genome gene expression (WGE) analyses through well-defined oligonucleotide microarray platforms represent a powerful tool for the molecular characterization of biological process. In the present manuscript, the utility of microarray technology is applied for the ACR and HCV-recurrence biological characterization in post-LT liver biopsy samples. Moreover, WGE analysis was performed to identify predictive biomarkers of HCV recurrence severity in formalin-fixed paraffin-embedded liver biopsies prospectively collected
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