Add to ORKG< ∞ when |α | ≤ m in which Ω is a bounded Lipschitz domain in Rn, ̺ is a rearrangement-invariant (r.i.) norm and 1 ≤ m ≤ n − 1. For such a space we have shown there exist r.i. norms, τ ̺ and σ̺, that are optimal with respect to the inclusions Wm,̺(Ω) ⊂Wm,τ ̺ (Ω) ⊂ Lσ ̺ (Ω). The aim of this paper is to give explicit formulas for τ ̺ and σ̺. Our approach is to use the techniques and results of Interpolation Theory. 1
Abstract. Compactness properties of Sobolev imbeddings are studied within the context of rearrangeme...
In this work, we study the behaviour of linear kernel operators on rearrange- ment-invariant (r.i.) ...
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...
AbstractWe give necessary and sufficient conditions for the set of measurable functions Y(A)={f:‖t−m...
ABSTRACT. Sobolev imbeddings (over suitable open subsets of Rn) can be extended from the classical L...
Let m and n be positive integers with n⩾2 and 1⩽m⩽n−1. We study rearrangement-invariant quasinorms ϱ...
AbstractLet m and n be positive integers with n⩾2 and 1⩽m⩽n−1. We study rearrangement-invariant quas...
We develop a new method of discretization and anti-discretization of weighted inequalities which we ...
We develop a new method of discretization and anti-discretization of weighted inequalities which we ...
The classical Gagliardo–Nirenberg interpolation inequality is a well-known estimate which gives, in ...
The classical Gagliardo–Nirenberg interpolation inequality is a well-known estimate which gives, in ...
AbstractLet F be a σ-algebra on [0, 1] generated by a countable partition of [0, 1], and let (·|F) d...
AbstractIn this paper the K-interpolation method of J. Peetre is built up for rearrangement invarian...
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on...
. Let m and n be positive integers with n 2 and 1 m n \Gamma 1. We study rearrangement-invariant ...
Abstract. Compactness properties of Sobolev imbeddings are studied within the context of rearrangeme...
In this work, we study the behaviour of linear kernel operators on rearrange- ment-invariant (r.i.) ...
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...
AbstractWe give necessary and sufficient conditions for the set of measurable functions Y(A)={f:‖t−m...
ABSTRACT. Sobolev imbeddings (over suitable open subsets of Rn) can be extended from the classical L...
Let m and n be positive integers with n⩾2 and 1⩽m⩽n−1. We study rearrangement-invariant quasinorms ϱ...
AbstractLet m and n be positive integers with n⩾2 and 1⩽m⩽n−1. We study rearrangement-invariant quas...
We develop a new method of discretization and anti-discretization of weighted inequalities which we ...
We develop a new method of discretization and anti-discretization of weighted inequalities which we ...
The classical Gagliardo–Nirenberg interpolation inequality is a well-known estimate which gives, in ...
The classical Gagliardo–Nirenberg interpolation inequality is a well-known estimate which gives, in ...
AbstractLet F be a σ-algebra on [0, 1] generated by a countable partition of [0, 1], and let (·|F) d...
AbstractIn this paper the K-interpolation method of J. Peetre is built up for rearrangement invarian...
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on...
. Let m and n be positive integers with n 2 and 1 m n \Gamma 1. We study rearrangement-invariant ...
Abstract. Compactness properties of Sobolev imbeddings are studied within the context of rearrangeme...
In this work, we study the behaviour of linear kernel operators on rearrange- ment-invariant (r.i.) ...
Consider p : Ω → [1,+∞[, a measurable bounded function on a bounded set Ω with decreasing rearrange...