scholarly journals Local Growth Envelopes of Besov Spaces of Generalized Smoothness

2006 ◽  
pp. 265-298
Author(s):  
Moulay Sidi Ammi ◽  
Walter Farkas
Keyword(s):  
Besov Spaces ◽  
Local Growth ◽  
Growth Envelopes

scholarly journals Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

2005 ◽  
Vol 3 (1) ◽  
pp. 33-71 ◽  
Author(s):  
António M. Caetano ◽  
Dorothee D. Haroske
Keyword(s):  
Asymptotic Behaviour ◽  
Function Spaces ◽  
Approximation Numbers ◽  
Local Growth ◽  
Recent Developments ◽  
Limiting Case ◽  
Growth Envelopes

Continuity envelopes for the spaces of generalised smoothnessBpq(s,Ψ)(ℝn)andFpq(s,Ψ)(ℝn)are studied in the so-called supercriticals=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.

scholarly journals Local growth envelopes of spaces of generalized smoothness: the subcriticalcase

2004 ◽  
Vol 273 (1) ◽  
pp. 43-57 ◽  
Author(s):  
António M. Caetano ◽  
Susana D. Moura
Keyword(s):  
Local Growth ◽  
Growth Envelopes

Local Growth Envelopes of Triebel-Lizorkin Spaces of Generalized Smoothness

2006 ◽  
Vol 12 (4) ◽  
pp. 427-445 ◽  
Author(s):  
António M. Caetano ◽  
Hans-Gerd Leopold
Keyword(s):  
Local Growth ◽  
Growth Envelopes

scholarly journals Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes

2009 ◽  
Vol 7 (3) ◽  
pp. 251-288 ◽  
Author(s):  
Cornelia Schneider
Keyword(s):  
Besov Spaces ◽  
Analytical Methods ◽  
Lorentz Spaces ◽  
Sobolev Type ◽  
Growth Envelopes

We characterize Triebel-Lizorkin spaces with positive smoothness onℝn, obtained by different approaches. First we present three settingsFp,qs(ℝn),Fp,qs(ℝn),ℑp,qs(ℝn)associated to definitions by differences, Fourier-analytical methods and subatomic decompositions. We study their connections and diversity, as well as embeddings between these spaces and into Lorentz spaces. Secondly, relying on previous results obtained for Besov spaces𝔅p,qs(ℝn), we determine their growth envelopes𝔈G(Fp,qs(ℝn))for0≺p≺∞,0≺q≤∞,s≻0, and finally discuss some applications.

Growth envelopes of Besov spaces on fractal h -sets

2012 ◽  
Vol 286 (5-6) ◽  
pp. 550-568 ◽  
Author(s):  
António M. Caetano
Keyword(s):  
Besov Spaces ◽  
Growth Envelopes

scholarly journals Besov spaces with positive smoothness on Rn, embeddings and growth envelopes

2009 ◽  
Vol 161 (2) ◽  
pp. 723-747 ◽  
Author(s):  
Dorothee D. Haroske ◽  
Cornelia Schneider
Keyword(s):  
Besov Spaces ◽  
Growth Envelopes

Diffraction from arrays of antiphase boundaries in ordered III-V alloys

1987 ◽  
Vol 45 ◽  
pp. 312-313
Author(s):  
T. S. Kuan
Keyword(s):  
High Surface ◽  
Growth Conditions ◽  
Ternary Alloys ◽  
Local Growth ◽  
Antiphase Boundaries ◽  
Surface Mobility ◽  
Ordered Phases ◽  
Diffraction Patterns ◽  
Atomically Flat ◽  
Degree Of Order

Recent electron diffraction studies have found ordered phases in AlxGa1-xAs, GaAsxSb1-x, and InxGa1-xAs alloy systems, and these ordered phases are likely to be found in many other III-V ternary alloys as well. The presence of ordered phases in these alloys was detected in the diffraction patterns through the appearance of superstructure reflections between the Bragg peaks (Fig. 1). The ordered phase observed in the AlxGa1-xAs and InxGa1-xAs systems is of the CuAu-I type, whereas in GaAsxSb1-x this phase and a chalcopyrite type ordered phase can be present simultaneously. The degree of order in these alloys is strongly dependent on the growth conditions, and during the growth of these alloys, high surface mobility of the depositing species is essential for the onset of ordering. Thus, the growth on atomically flat (110) surfaces usually produces much stronger ordering than the growth on (100) surfaces. The degree of order is also affected by the presence of antiphase boundaries (APBs) in the ordered phase. As shown in Fig. 2(a), a perfectly ordered In0.5Ga0.5As structure grown along the <110> direction consists of alternating InAs and GaAs monolayers, but due to local growth fluctuations, two types of APBs can occur: one involves two consecutive InAs monolayers and the other involves two consecutive GaAs monolayers.

Flame Synthesis of ZnO Nanostructures: Morphology and Local Growth Conditions

2008 ◽  
Author(s):  
Stephen Tse ◽  
Fusheng Xu ◽  
Cassandra D'Esposito ◽  
Xiaofei Liu ◽  
Bernard Kear
Keyword(s):  
Growth Conditions ◽  
Flame Synthesis ◽  
Zno Nanostructures ◽  
Local Growth
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