The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950'...The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper, we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces(of fractional order of smoothness),based on integral averages on dyadic cubes, which is well-adapted to extending functions using the Whitney extension operator.展开更多
In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spac...In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.展开更多
In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract ...In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.展开更多
基金supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Grant No. 307333)
文摘The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper, we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces(of fractional order of smoothness),based on integral averages on dyadic cubes, which is well-adapted to extending functions using the Whitney extension operator.
基金partly supported by NNSF of China(Grant No.11822105)partly supported by NNSF of China(Grant Nos.12071121 and 11720101003)supported by NNSF of China(Grant No.12101226)。
文摘In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.
文摘In this paper,we show that the elliptic cocenter of the Hecke algebra of a con-nected reductive p-adic group is contained in the rigid cocenter.As applications,we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l representations.
