On rearrangement-invariant hull of generalized Sobolev spaces

The equivalent description of decreasing rearrangement cone is established for the function from Sobolev space W(dot)m E(Ω), where m∈N, Ω - a bounded open domain in Rn, E=E(Ω) - rearrangement-invariant space. On its base the description of rearrangement-invariant hull of Sobolev space is given, that is the minimal rearrangement-invariant space in which the Sobolev space is embedded

On rearrangement invariant hull of generalized Sobolev spaces

In this paper, an equivalent description of the cone of decreasing rearrangements for functions from the Sobolev space ẆE m(Ω), where m ∈ N, Ω is an open bounded domain in Rn, and E = E(Ω) is a rearrangement invariant space is given. It is used to describe the rearrangement invariant hull of the Sobolev space, i.e., the minimal invariant rearrangement space in which the Sobolev space is embedded. Copyright © 2005 by Pleiades Publishing, Inc

Estimates of norms of hardy-type integral and discrete operators on cones of quasimonotone functions

[No abstract available

Estimates of norms of hardy-type integral and discrete operators on cones of quasimonotone functions

[No abstract available

О ПЕРЕСТАНОВОЧНО-ИНВАРИАНТНОЙ ОБОЛОЧКЕ ОБОБЩЕННЫХ ПРОСТРАНСТВ СОБОЛЕВА

The equivalent description of decreasing rearrangement cone is established for the function from Sobolev space W(dot)m E(Ω), where m∈N, Ω - a bounded open domain in Rn, E=E(Ω) - rearrangement-invariant space. On its base the description of rearrangement-invariant hull of Sobolev space is given, that is the minimal rearrangement-invariant space in which the Sobolev space is embedded

Integral properties of generalized Bessel potentials

The study on the space of generalized Besel potentials in Euclidean n-space Rn is discussed. The Euclidian n-space is defined as a function of Besel-Macdonald kernel and Macdonald function. The rearrangement invariant space (RIS) class includes the Lp, Lorentz, Marcinkiewicz, and Orlicz spaces. Embedding theory for classical Besel potentials and their weighted generalizations is exposed in Maz'ya's survey. The problems are posed by Netrusov. An important role is played by estimates for convolution decreasing rearrangements obtained by O'Neil. The results are concretized and the rearrangement invariant hull of the potential space is described

Local growth envelopes and optimal embeddings of generalized Sobolev spaces

The order-sharp estimates for the local growth envelopes of functions from the generalized Sobolev spaces are obtained, and an explicit description of the rearrangement-invariant hulls of the generalized Lorentz-Sobolev spaces, is also presented. It was assumed that the norm of any function from a rearrangement-invariant space (RIS) can be represented in terms of its rearrangement. Such a representation is known as the Luxemburg representation. A positive function is said to be essentially decreasing if it satisfies the monotonically inequality with some positive constant, not necessarily equal to 1. The interpretation of the notion of a RIS followed the axiomatics suggested by Bennet and Sharpley

Local growth envelopes and optimal embeddings of generalized Sobolev spaces

The order-sharp estimates for the local growth envelopes of functions from the generalized Sobolev spaces are obtained, and an explicit description of the rearrangement-invariant hulls of the generalized Lorentz-Sobolev spaces, is also presented. It was assumed that the norm of any function from a rearrangement-invariant space (RIS) can be represented in terms of its rearrangement. Such a representation is known as the Luxemburg representation. A positive function is said to be essentially decreasing if it satisfies the monotonically inequality with some positive constant, not necessarily equal to 1. The interpretation of the notion of a RIS followed the axiomatics suggested by Bennet and Sharpley

Integral properties of generalized Bessel potentials

The study on the space of generalized Besel potentials in Euclidean n-space Rn is discussed. The Euclidian n-space is defined as a function of Besel-Macdonald kernel and Macdonald function. The rearrangement invariant space (RIS) class includes the Lp, Lorentz, Marcinkiewicz, and Orlicz spaces. Embedding theory for classical Besel potentials and their weighted generalizations is exposed in Maz'ya's survey. The problems are posed by Netrusov. An important role is played by estimates for convolution decreasing rearrangements obtained by O'Neil. The results are concretized and the rearrangement invariant hull of the potential space is described

On rearrangement invariant hull of generalized Sobolev spaces

In this paper, an equivalent description of the cone of decreasing rearrangements for functions from the Sobolev space ẆE m(Ω), where m ∈ N, Ω is an open bounded domain in Rn, and E = E(Ω) is a rearrangement invariant space is given. It is used to describe the rearrangement invariant hull of the Sobolev space, i.e., the minimal invariant rearrangement space in which the Sobolev space is embedded. Copyright © 2005 by Pleiades Publishing, Inc