In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators Re(λ) 1/2C(λ+A)−1, Re(λ) > 0 on the complex right half plane and weak Lebesgue L2,∞–admissibility are equivalent. Moreover, we show that the weak Lebesgue norm is best possible in the sense that it is the endpoint for the ’Weiss conjecture’ within the scale of Lorentz spaces L...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

background studies show that a large proportion of healthcare offered may be inappropriate or unnecessary. magnetic resonance imaging (mri) is a new and expensive diagnostic technology which has been increasingly used all over the world. moreover, this trend has been more rapidly increasing in iran. low back pain is a common disorder all over the world and mri technique is one of the several wa...

soil erosion is a serious problem especially in northern parts of iran. one themost important side effects on soil erosion may be the decline in qualities of soil refers toagricultural productivity. so it is very important to assess the soil erosion risk for thesustainable development of agriculture. this study outlines ways undertaken to provide anew tool to manage water erosion from physical ...

and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫

Reliability and validity are crucial issues in research. Reliability is concerned with lowered quality of data due to random errors in measurement. Validity is concerned with whether variables measure what they purport to measure or are biased by other systemic factors, excluding random errors. Strength of correlation is limited by reliability. Given the problems in measuring reliability and va...

In the preceding chapters, the effects of lensing were so strong as to leave an unmistakable imprint on a specific source, allowing a detailed treatment. However, only the densest regions of the universe are able to provide such a spectacular lensing effect. To study more representative regions of the universe, we must examine large numbers of sources statistically. This is the domain of weak l...