EuDML | Browse

We prove some exact formulas for the E and K functionals for pairs of the type (X(A),l sub ∞ (B)) where X has the lattice property. These formulas are extensions of their well-known counterparts in the scalar valued case. In particular we generalize formulas by Pisier and by the present author.

The equation $- Δ 𝑢 - λ \frac{𝑢}{{| 𝑥 |}^{2}} = {| \nabla 𝑢 |}^{𝑝} + 𝑐 𝑓 (𝑥)$ : The optimal power

Boumediene Abdellaoui, Ireneo Peral (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We will consider the following problem $- Δ u - λ \frac{u}{{| x |}^{2}} = {| \nabla u |}^{p} + c f, u > 0 in Ω,$ where $Ω \subset ℝ^{N}$ is a domain such that $0 \in Ω$ , $N \geq 3$ , $c > 0$ and $λ > 0$ . The main objective of this note is to study the precise threshold $p_{+} = p_{+} (λ)$ for which there is novery weak supersolutionif $p \geq p_{+} (λ)$ . The optimality of $p_{+} (λ)$ is also proved by showing the solvability of the Dirichlet problem when $1 \leq p < p_{+} (λ)$ , for $c > 0$ small enough and $f \geq 0$ under some hypotheses that we will prescribe.

The Euler-Lagrange inclusion in Orlicz-Sobolev spaces

Hôǹg Thái Nguyêñ, Dariusz Pączka (2014)

Banach Center Publications

We establish the Euler-Lagrange inclusion of a nonsmooth integral functional defined on Orlicz-Sobolev spaces. This result is achieved through variational techniques in nonsmooth analysis and an integral representation formula for the Clarke generalized gradient of locally Lipschitz integral functionals defined on Orlicz spaces.

The exact value of Jung constants in a class of Orlicz function spaces.

Y. Q. Yan (2005)

Collectanea Mathematica

Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value:(i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 < CΦ < 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1;(ii) If FΦ(t) is increasing and CΦ > 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1])=2-1/CΦ,where CΦ= limt→+∞ tφ(t)/Φ(t).

The existence in every separable Banach space of a fundamental total and bounded biorthogonal sequence and related constructions of uniformly bounded orthonormal systems in $L^{2}$

R. I. Ovsepian, A. Pełczyński (1973/1974)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

The Fourier transform in weighted Lorenz spaces.

Gord Sinnamon (2003)

Publicacions Matemàtiques

The fractional integral between weighted Orlicz and $B M O_{φ}$ spaces on spaces of homogeneous type

Gladis Pradolini, Oscar Salinas (2003)

Commentationes Mathematicae Universitatis Carolinae

In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable $B M O_{φ}$ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted $L^{p}$ and Lipschitz integral spaces on $ℝ^{n}$ . We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.

The Functional Equation

Pavlos Sinopoulos (1987)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The general form of local bilinear functions

Milan Práger (1993)

Applications of Mathematics

The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces $L_{2} (a, b)$ and $H^{1} (a, b)$ is given.

Currently displaying 21 – 40 of 105

Previous Page 2 Next

Displaying 21 – 40 of 105

The criteria of strongly exposed points in Orlicz spaces

The differences of inclusion map operators between rearrangement invariant spaces on finite and sigma-finite measure spaces.

The distribution of non-commutative Rademacher series.

The dual and bidual of an echelon Köthe space.

The Dual Ball of a Lindenstrauss Space.

The dual of the space of measures with continuous translations.

The dual of weak $L^{p}$

The E and K functionals for the pair (X (A), l∞(B)).

The equation $- Δ 𝑢 - λ \frac{𝑢}{{| 𝑥 |}^{2}} = {| \nabla 𝑢 |}^{𝑝} + 𝑐 𝑓 (𝑥)$ : The optimal power

The Euler-Lagrange inclusion in Orlicz-Sobolev spaces

The exact value of Jung constants in a class of Orlicz function spaces.

The existence in every separable Banach space of a fundamental total and bounded biorthogonal sequence and related constructions of uniformly bounded orthonormal systems in $L^{2}$

The Fourier transform in weighted Lorenz spaces.

The fractional integral between weighted Orlicz and $B M O_{φ}$ spaces on spaces of homogeneous type

The Functional Equation

The general form of local bilinear functions

The generalization of Cellina's Fixed Point Theorem

The generalized Hardy operator with kernel and variable integral limits in Banach function spaces.

The heredity problem for weakly compactly generated Banach spaces

The Hölder duality for harmonic functions

Currently displaying 21 – 40 of 105