We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical space...We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.展开更多
The number of patients suffering from symptoms associated with gastrointestinal(GI) motility disorders is on the rise. GI motility disorders are accompanied by alteration of gastrointestinal smooth muscle functions. C...The number of patients suffering from symptoms associated with gastrointestinal(GI) motility disorders is on the rise. GI motility disorders are accompanied by alteration of gastrointestinal smooth muscle functions. Currently available drugs,which can directly affect gastrointestinal smooth muscle and restore altered smooth muscle contractility to normal,are not satisfactory for treating patients with GI motility disorders. We have recently shown that ERK1/2 and p38MAPK signaling pathways play an important role in the contractile response not only of normal intestinal smooth muscle but also of inflamed intestinal smooth muscle. Here we discuss the possibility that ERK1/2 and p38MAPK signaling pathways represent ideal targets for generation of novel therapeutics for patients with GI motility disorders.展开更多
基金supported by University of Cyprus and New Function Spaces in Harmonic Analysis and Their Applications in Statistics(Individual Grant)。
文摘We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.
基金Supported by the Research Grant from the Canadian Institutes for Health Research,and Partly by an Alberta Innovates-Health Solutions Senior Scholar Award and Canada Research Chair in Smooth Muscle Pathophysiology
文摘The number of patients suffering from symptoms associated with gastrointestinal(GI) motility disorders is on the rise. GI motility disorders are accompanied by alteration of gastrointestinal smooth muscle functions. Currently available drugs,which can directly affect gastrointestinal smooth muscle and restore altered smooth muscle contractility to normal,are not satisfactory for treating patients with GI motility disorders. We have recently shown that ERK1/2 and p38MAPK signaling pathways play an important role in the contractile response not only of normal intestinal smooth muscle but also of inflamed intestinal smooth muscle. Here we discuss the possibility that ERK1/2 and p38MAPK signaling pathways represent ideal targets for generation of novel therapeutics for patients with GI motility disorders.
