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Integral inequalities and summability of solutions of some differential problems

Lucio Boccardo (2000)

Banach Center Publications

The aim of this note is to indicate how inequalities concerning the integral of ${| \nabla u |}^{2}$ on the subsets where |u(x)| is greater than k ( $k \in I R^{+}$ ) can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of ${| \nabla u |}^{2}$ on the subsets where |u(x)| is less than k ( $k \in I R^{+}$ ) or...

Integral operators and absolute convergence systems.

Korotkov, V.B. (2002)

Sibirskij Matematicheskij Zhurnal

Integral representation of additive transformations on $L_{p}$ spaces

Utpal Bandyopadhyay (1973)

Studia Mathematica

Integral representations and transforms of $N$ -functions. I.

Mamontov, A.E. (2006)

Sibirskij Matematicheskij Zhurnal

Integral representations and transforms of $N$ -functions. II.

Mamontov, A.E. (2006)

Sibirskij Matematicheskij Zhurnal

Intégration non commutative représentation projective d’espaces $L^{p}$

Daniel Kalnins (1977/1978)

Séminaire Paul Krée

Intermediate spaces and the complex method of interpolation for families of Banach spaces

Eugenio Hernández (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Interpolation between Hardy spaces on the bidisc

Kai-Ching Lin (1986)

Studia Mathematica

Interpolation of $2^{n}$ Banach spaces

Dicesar Fernandez (1979)

Studia Mathematica

Interpolation of bilinear operators between Banach function spaces.

Mieczyslaw Mastylo, Dariusz Staszak (1999)

Collectanea Mathematica

Interpolation of Cesàro sequence and function spaces

Sergey V. Astashkin, Lech Maligranda (2013)

Studia Mathematica

The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that $C e s_{p} (I)$ is an interpolation space between $C e s_{p ₀} (I)$ and $C e s_{p ₁} (I)$ for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, $C e s_{p} [0, 1]$ is not an interpolation space between Ces₁[0,1] and $C e s_{\infty} [0, 1]$ .

Interpolation of Marcinkiewicz spaces.

Michael Cwikel, Per Nilsson (1985)

Mathematica Scandinavica

Interpolation of operations and Orlicz classes

Alberto Torchinsky (1976)

Studia Mathematica

Interpolation of Operators on Decreasing Functions.

John Cerda, Joaquim Martin (1996)

Mathematica Scandinavica

Interpolation of operators when the extreme spaces are $L^{\infty}$

Jesús Bastero, Francisco Ruiz (1993)

Studia Mathematica

Under some assumptions on the pair $(A_{0}, B_{0})$ , we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are $L^{\infty}$ . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.

Interpolation of Orlicz spaces

Jan Gustavsson, Jaak Peetre (1977)

Studia Mathematica

Interpolation of Orlicz-valued function spaces and U.M.D. property

D. Fernandez, J. Garcia (1991)

Studia Mathematica

Interpolation of quasicontinuous functions

Joan Cerdà, Joaquim Martín, Pilar Silvestre (2011)

Banach Center Publications

If C is a capacity on a measurable space, we prove that the restriction of the K-functional $K (t, f; L^{p} (C), L^{\infty} (C))$ to quasicontinuous functions f ∈ QC is equivalent to $K (t, f; L^{p} (C) \cap Q C, L^{\infty} (C) \cap Q C)$ . We apply this result to identify the interpolation space ${(L^{p ₀, q ₀} (C) \cap Q C, L^{p ₁, q ₁} (C) \cap Q C)}_{θ, q}$ .

Interpolation of r-Banach spaces

Yoram Sagher (1972)

Studia Mathematica

Interpolation of Spectral Operators.

Kandiah Dayanithy (1978)

Mathematische Zeitschrift

Currently displaying 21 – 40 of 62

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