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1. Boundedness and compactness of the embedding between spaces with multiweighted derivatives when $1 \leq q < p <\infty $

Creator:
Abdikalikova, Zamira, Oinarov, Ryskul, and Persson, Lars-Erik
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
weighted function space, multiweighted derivative, embedding theorems, and compactness
Language:
English
Description:
We consider a new Sobolev type function space called the space with multiweighted derivatives $W_{p,\bar {\alpha }}^n$, where $\bar {\alpha } = (\alpha _0, \alpha _1, \ldots , \alpha _n)$, $\alpha _i \in \Bbb R$, $i=0,1, \ldots , n$, and $\|f\|_{W_{p,{\bar \alpha }}^n} = \|D_{{\bar \alpha }}^n f\|_p + \sum _{i=0}^{n-1} |D_{\bar \alpha }^i f(1)|$, $$ D_{{\bar \alpha }}^0 f(t) = t^{\alpha _0} f(t), \quad D_{{\bar \alpha }}^i f(t) = t^{\alpha _i} \frac {{\rm d}}{{\rm d}t} D_{{\bar \alpha }}^{i-1} f(t), \enspace i=1, 2, \ldots , n. $$ We establish necessary and sufficient conditions for the boundedness and compactness of the embedding $W_{p,{\bar \alpha }}^n \hookrightarrow W_{q,{\bar \beta }}^m $, when $1 \leq q < p < \infty $, $0\leq m <n$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. La question de la « ville-résidence », « ville-capitale » et « ville de couronnement » dans la Hongrie de Marie-Thérèse et le projet d’extension de la ville de Presbourg des années 1774-1779

Creator:
Mureşan, Raluca
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
capitality, urban embellishment, coronation sites, kingdom of Hungary, Maria Theresa, and Pressburg
Language:
Czech
Description:
This paper sheds light on the architectural representation of capitality issues in the Habsburg Monarchy. It focuses on one particular case study: the enlargement and embellishment project for the city of Pressburg (Bratislava) realized between 1774 and 1779. The city hosted the coronations of the Habsburgs as kings of Hungary, was the seat of the central administration of the kingdom since 1536, and from 1760 housed the main residence of the royal lieutenants, the Duke of Saxony-Teschen and the Archduchess Maria-Christina. The aim of this contribution is to show how these three functionally differentiated capitality aspects were actively displayed in the newly created urban space. Focusing on issues of patronage, this study stresses the role of each statesman in the decision-making process and explores in detail the networks drawn between statesmen serving the Lieutenancy Council of Hungary, the Royal Chamber, the royallieutenant Duke of Saxony-Teschen, and Maria-Theresa herself. The main initiators of the embellishment works were the Hungarian statesmen working in the central administration, notably the counsellor Count György Csáky, supported by the Duke of Saxony- Teschen. Csáky directed the embellishment project on behalf of the Lieutenancy Council, while at the same time building a theatre at his own expense in the same area. and Besides embellishing and extending the city, works carried out in 1774-1779 were meant to have visible consequences for future coronation celebrations: they modified the procession route; and they emphasised the moment of the king’s oath to defend the kingdom by building a permanent platform made of stone, the Königsberg. In this way, the embellishment project marked the characteristics of Hungarian coronations, while at the same time transforming the symbolic reference to the former coronation sites in Székesfehérvár. On the other hand, the newly created cathedral square, as well as the architecture of the theatre built by Count Csáky, reflected the presence of the archducal court – in other words, the quality of “residence city” that had been previously emphasized only by the reconstruction of the castle on behalf of the Imperial Chamber. We are thus reminded that the Pressburg embellishment project, with its emphasis on the attributes of capitality in urban space, was constantly the subject of renegotiations and hierarchical rankings meant to reflect local, regional, central and dynastical interests.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public