Isometries of Hp Spaces of Bounded Symmetric Domains

1976 ◽  
Vol 28 (2) ◽  
pp. 334-340 ◽  
Author(s):  
Adam Korányi ◽  
Stephen Vági
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Unit Disc ◽  
The State ◽  
Bounded Symmetric Domains ◽  
Several Variables ◽  
Hp Spaces ◽  
State Of Affairs

The isometries of the Hardy spaces Hv (0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in 1964 [3]. For p = 1 the result had been found earlier by deLeeuw, Rudin and Wermer [2]. For several variables the state of affairs at present is this: For the polydisc the isometries of Hp onto itself have been characterized by Schneider [13]. For the unit ball the same result was proved in the case p > 2 by Forelli [4]. Finally in [12] Rudin removed the restriction p > 2 and also established some results about isometries of Hp of the ball and the polydisc into itself.

Isometries of Bergman Spaces over Bounded Runge Domains

1981 ◽  
Vol 33 (5) ◽  
pp. 1157-1164 ◽  
Author(s):  
Clinton J. Kolaski
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Bounded Symmetric Domains ◽  
Several Variables ◽  
Special Cases

1.1. The isometries of the Hardy spaces Hp(0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in [2]. Generalizations to several variables: For the polydisc the isometries of Hp onto itself were characterized by Schneider [9]. For the unit ball the case p > 2 was then done by Forelli [3]; Rudin [8] removed the restriction p > 2 by proving a theorem on equimeasurability. Finally, Koranyi and Vagi [6] noted that the methods developed by Forelli, Rudin and Schneider applied to bounded symmetric domains.In this note it will be shown that their methods also apply to the Bergman spaces over bounded Runge domains. The isometries which are onto are completely characterized; the special cases of the ball and polydisc are particularly nice and are given separately.

scholarly journals Independent inner functions in the classical domains

1987 ◽  
Vol 29 (2) ◽  
pp. 229-236
Author(s):  
Tomasz M. Wolniewicz
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Isometric Embedding ◽  
Symmetric Domain ◽  
Type I ◽  
Bounded Symmetric Domains ◽  
Inner Functions ◽  
Main Result Theorem ◽  
Complemented Subspace ◽  
Result Theorem

Let Bn denote the unit ball and Un the unit polydisc in Cn. In this paper we consider questions concerned with inner functions and embeddings of Hardy spaces over bounded symmetric domains. The main result (Theorem 2) states that for a classical symmetric domain D of type I and rank(D) = s, there exists an isometric embedding of Hl(Us) onto a complemented subspace of Hl(D). This should be compared with results of Wojtaszczyk [13] and Bourgain [3, 4] which state that H1(Bn) is isomorphic to Hl(U) while for n>m, Hl(Un) cannot be isomorphically embedded onto a complemented subspace of H1(Um). Since balls are the only bounded symmetric domains of rank 1 and they are of type I, Theorem 2 shows that if rank(D1) = 1, rank(D2) > 1 then H1(D1) is not isomorphic to H1(D2). It is natural to expect this to hold always when rank(D1 ≠ rank(D2) but unfortunately we were not able to prove this.

A Better Solution to the General Problem of Creation

2017 ◽  
Vol 9 (1) ◽  
pp. 147-162
Author(s):  
Jeremy W. Skrzypek
Keyword(s):  
Recent Work ◽  
General Problem ◽  
The State ◽  
State Of Affairs ◽  
Better Than

It is often suggested that, since the state of affairs in which God creates a good universe is better than the state of affairs in which He creates nothing, a perfectly good God would have to create that good universe. Making use of recent work by Christine Korgaard on the relational nature of the good, I argue that the state of affairs in which God creates is actually not better, due to the fact that it is not better for anyone or anything in particular. Hence, even a perfectly good God would not be compelled to create a good universe.

A model of the analysis of the dynamics and structure of socio-economic development (an example of the set of the largest Polish cities in the years 1998–2015)

2019 ◽  
Vol 63 (1) ◽  
pp. 25-37
Author(s):  
Lidia Mierzejewska ◽  
Jerzy Parysek
Keyword(s):  
Principal Component Analysis ◽  
Economic Development ◽  
Development Process ◽  
Principal Component ◽  
The State ◽  
Geographical Research ◽  
Development Policies ◽  
Socio Economic Development ◽  
Development Processes ◽  
State Of Affairs

Abstract The complexity of the reality studied by geographical research requires applying such methods which allow describing the state of affairs and ongoing changes in the best possible way. This study aims to present a model of research on selected aspects of the dynamics and structure of socio-economic development. The idea was to determine whether we deal with the process of reducing or widening the differences in terms of individual features. The article primarily pursues a methodological goal, and to a lesser extent an empirical one. The methodological objective of the paper was to propose and verify a multi-aspect approach to the study of development processes. The analyses carried out reveal that in terms of the features taken into account in the set of 24 of the largest Polish cities the dominating processes are those increasing differences between cities, which are unfavourable in the context of the adopted development policies aiming at reducing the existing disparities. In relation to the methodological objective, the results of the conducted research confirm the rationale of the application of the measures of dynamics and the feature variance to determine the character (dynamics and structure) of the socio-economic development process of cities. Comparatively less effective, especially for interpretation, is the application of principal component analysis and a multivariate classification, which is mainly the result of differences in the variance of particular features.

Development of Interethnic Relations in Bosnia and Herzegovina in the First Decades after the Second World War

2018 ◽  
Vol 13 (3-4) ◽  
pp. 87-96
Author(s):  
Elena Yu. Guskova
Keyword(s):  
Ethnic Identity ◽  
Bosnia And Herzegovina ◽  
Second World War ◽  
The State ◽  
World War ◽  
Interethnic Relations ◽  
The Republic ◽  
State Of Affairs ◽  
First Time ◽  
Second World

The article is devoted to the analysis of interethnic relations in Bosnia and Herzegovina (BiH) in the 1940s and 1960s. The article is based on materials from the archives of BiH, Croatia, Slovenia, Yugoslavia. The documents show the state of affairs in the Republic – both in the economy and in ideology. In one or another way, all of them reflect the level of tension in the interethnic relations. For the first time, the article presents the discussion on interethnic relations, on the new phenomenon in multinational Yugoslavia – the emergence of a new people in BiH under the name of “Muslim”. The term “Muslims” is used to define the ethnic identity of Bosniaks in the territory of BiH starting from the 1961 census.

The State as an Actor

2017 ◽  
Author(s):  
Georg Menz
Keyword(s):  
Service Sector ◽  
The State ◽  
The Political ◽  
Regulatory Capture ◽  
Banking Institutions ◽  
Political Left ◽  
Central Actor ◽  
Capitalist State ◽  
State Of Affairs ◽  
Rules Of The Game

Despite the state being such a central actor in establishing and policing the rules of the game of any given political economy, its role is often neglected. In this chapter, we briefly review relevant state theories and explore changes to the nature and appearance of the capitalist state. The awesome increase in the political fire power of the financial service sector has unfortunately led to regulatory capture. The state can no longer be considered a neutral umpire, being heavily influenced by the prerogatives of major banking institutions. This state of affairs corrupts the hopes that liberals place in the self-policing powers of the marketplace and reflects certain fears on the political left regarding the pernicious effects of ‘financialization’.

Plebiscitary Politics and the Threats to Legality

2019 ◽  
pp. 275-289
Author(s):  
Claudius Härpfer
Keyword(s):  
The State ◽  
Short Term ◽  
Political Processes ◽  
The Face ◽  
State Of Affairs ◽  
The Relationship

In recent times we find many plebiscitary acts that seek to democratically legitimize political processes in any direction. They have in common that they interrupt the normal routine of representative democracies to a certain degree and create an extra-daily state of affairs, which entails not only direct but also indirect consequences. The text attempts to systematize some of these mechanisms from a Weberian perspective using Brexit as an example. After a brief overview of Weber’s short-term politically inspired statements on plebiscitary democracy, the text systematizes Weber’s understanding of the state as a bureaucratic apparatus that requires any kind of leader to be controlled. Subsequently, the text discusses the relationship between domination, legality, and rationality in order to finally point out the danger of erosion of truth and legality through the emergence of competing consensus communities in the face of competing conceptions of order.

Letters to the Editor

PEDIATRICS ◽  
1964 ◽  
Vol 34 (3) ◽  
pp. 439-439
Author(s):  
LAURENCE FINBERG
Keyword(s):  
Whooping Cough ◽  
Etiologic Agent ◽  
The State ◽  
Letters To The Editor ◽  
State Of Affairs ◽  
The One ◽  
Made In

Dr. Jaffe is, of course, correct that it is often possible to culture H. pertussis from patients with whooping cough. Our statement in the paper referred to the facts as they are for our series, even though we regret the state of affairs. We therefore very carefully listed the criteria by which the diagnosis was made in the absence of finding the specific etiologic agent. The method referred to by Dr. Jaffe for culturing the organisms was not the one that was employed by the Bacteriology Laboratory of the hospital.

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