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Spaces defined by the level function and their duals

100%

Sinnamon G.

Studia Mathematica

1994

tom 111

nr 1

19-52

The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.

A note on multivariate variants of Hardy's inequality

88%

Pachpatte B. G.

Fasciculi Mathematici

1999

tom Nr 30

107-112

In the present note we establish multivariate generalizations of the certain variants ofthe well known Hardy's inequality. Our results are obtained by using the well known Fubini's theorem.

Harmonic vibration of cusped plates in the N-th approximation of Vekua’s hierarchical models

75%

Chinchaladze N.

Archives of Mechanics

2013

tom Vol. 65, nr 5

345--365

In this paper elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the N-th approximation of Vekua’s hierarchical models are considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The classical and weak setting of the BVPs in the case of the N-th approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established.