Rough Maximal Oscillatory Singular Integral Operators

2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are established

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Maximal-Element Rationalizability

We examine the maximal-element rationalizability of choice functions with arbitrary do-mains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier litera-ture, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationaliz-ability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as re exivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Nutritional regulation of the fatty acid synthase promoter in vivo: Sterol regulatory element binding protein functions through an upstream region containing a sterol regulatory element

The transcription of fatty acid synthase (FAS), a central enzyme in de novo lipogenesis, is dramatically induced by fasting/refeeding and insulin. We reported that upstream stimulatory factor binding to the −65 E-box is required for induction of the FAS transcription by insulin in 3T3-L1 adipocytes. On the other hand, we recently found that two upstream 5′ regions are required for induction in vivo by fasting/refeeding and insulin; one at −278 to −131 albeit at a low level, and the other at −444 to −278 with an E-box at −332 where upstream stimulatory factor functions for maximal induction. Here, we generated double transgenic mice carrying the chloramphenicol acetyltransferase reporter driven by the various 5′ deletions of the FAS promoter region and a truncated active form of the sterol regulatory element (SRE) binding protein (SREBP)-1a. We found that SREBP participates in the nutritional regulation of the FAS promoter and that the region between −278 and −131 bp is required for SREBP function. We demonstrate that SREBP binds the −150 canonical SRE present between −278 and −131, and SREBP can function through the −150 SRE in cultured cells. These in vivo and in vitro results indicate that SREBP is involved in the nutritional induction of the FAS promoter via the −278/−131 region and that the −150 SRE is the target sequence.

Inhibition of G-protein betagamma-subunit functions by phosducin-like protein.

Phosducin is a cytosolic protein predominantly expressed in the retina and the pineal gland that can interact with the betagamma subunits of guanine nucleotide binding proteins (G proteins) and thereby may regulate transmembrane signaling. A cDNA encoding a phosducin-like protein (PhLP) has recently been isolated from rat brain [Miles, M. F., Barhite, S., Sganga, M. & Elliott, M. (1993) Proc. Natl. Acad. Sci. USA 90, 10831-10835. Here we report the expression of PhLP in Escherichia coli and its purification. Recombinant purified PUP inhibited multiple effects of G-protein betagamma subunits. First, it inhibited the betagamma-subunit-dependent ADP-ribosylation of purified alpha(o) by pertussis toxin. Second, it inhibited the GTPase activity of purified G(o). The IC50 value of PhLP in the latter assay was 89 nM, whereas phosducin caused half-maximal inhibition at 17 nM. And finally, PhLP antagonized the enhancement of rhodopsin phosphorylation by purified betagamma subunits. The N terminus of PhLP shows no similarity to the much longer N terminus of phosducin, the region shown to be critical for phosducin-betagamma-subunit interactions. Therefore, PhLP appears to bind to G-protein betagamma subunits by an as yet unknown mode of interaction and may represent an endogenous regulator of G-protein function.

A Recession Notion for a Class of Monotone Bivariate Functions

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.