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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . The Johns Hopkins University Press is collaborating with JSTOR to digitize, preserve and extend access to American Journal of Mathematics. Introduction. This paper deals with the connections between an analytic function f on the unit disc A in the complex plane and the membership in some Schatten ideal of the Hankel operator that f induces on certain weighted Bergman spaces of analytic functions on A. The general theme is the interplay between smoothness or growth conditions on f and the size of the s-numbers of the Hankel operator induced by f. Such themes have appeared before in connection with Hankel operators on the Hardy space H2 and a portion of the results here parallel those. These results may be found in the papers of V. V. Peller [24], [25], [26], R. Rochberg [27], [28], and S. Semmes [31]. In our context, however, an entirely new phenomena occurs at the lower end point, where the Macaev ideal appears in place of the nuclear operators. The appearance of the Macaev ideal requires the introduction of some new interpolation results to prove the intermediate results since the lower end point condition is not properly structured for interpolation. Important roles throughout the paper are played by the Mobius group and various spaces of functions invariant under it.The paper is arranged in the following manner. Section 1 introduces all the relevent definitions and background material and closes with statement of the main theorem. Section 2 is devoted to general properties of Hankel operators and describes an invariance of the action of the Mobius group on a Hankel operator. Section 3 contains the description of the Hankel operators with monomial symbols acting on other monomials and, as a consequence, establishes an isometry between the Dirichlet space and those Hankel operators that are Hilbert-Schmidt. Section 4 gives the characterization of bounded and compact Hankel operators; this result was nroved first by S. Axler [6] in a special but representative case. Section 5

This article develops and tests a set of theoretical mechanisms by which candidate ethnicity may have affected the party vote choice of both white British and ethnic minority voters in the 2010 British general election. Ethnic minority candidates suffered an average electoral penalty of about 4 per cent of the three-party vote from whites, mostly because those with anti-immigrant feelings were less willing to vote for Muslims. Ethnic minority voter responses to candidate ethnicity differed by ethnic group. There were no significant effects for non-Muslim Indian and black voters, while Pakistani candidates benefited from an 8-point average electoral bonus from Pakistani voters.Ethnic minorities are consistently under-represented in all democracies, 1 perhaps in part because majority voters discriminate against minority candidates. 2 Conversely, some research shows that visible minorities are more likely to vote for members of their own ethnic or racial group in the United States 3 and in proportional representation systems that allow preference voting. 4 While there is also evidence that candidate ethnicity affects voting in British elections, with one exception 5 this evidence has thus far been based on aggregate data or qualitative reports. There are also some interesting questions about the effects of candidate ethnicity that arise from the British context that can only now be addressed with high-quality individual-level survey data from the 2010 Ethnic Minority British Election Study. This article considers whether white British voters are more reluctant to vote for non-white candidates, and whether ethnic minority voters are more inclined to support non-white candidates, perhaps especially those from the same ethnic group.White British people perceive different minority groups differently, and Muslims receive among the most hostile reactions. 6 The terrorist attacks of