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Narrow operators (a survey)

Mikhail Popov (2011)

Banach Center Publications

Narrow operators are those operators defined on function spaces which are "small" at signs, i.e., at {-1,0,1}-valued functions. We summarize here some results and problems on them. One of the most interesting things is that if E has an unconditional basis then each operator on E is a sum of two narrow operators, while the sum of two narrow operators on L₁ is narrow. Recently this notion was generalized to vector lattices. This generalization explained the phenomena of sums: the set of all regular...

Near isometries of spaces of weak * continuous functions, with an application to Bochner spaces

Michael Cambern (1987)

Studia Mathematica

Nearly smooth points and near smoothness in Orlicz spaces

Ji Donghai, Yanming Lü, Ting Fu Wang (1998)

Commentationes Mathematicae Universitatis Carolinae

Nearly smooth points and near smoothness in Orlicz spaces are characterized. It is worth to notice that in the nonatomic case smooth points and nearly smooth points are the same, but in the sequence case they differ.

Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces

Viktor I. Burenkov, Huseyn V. Guliyev (2004)

Studia Mathematica

The problem of boundedness of...

Necessary and sufficient conditions for the boundedness of Dunkl-type fractional maximal operator in the Dunkl-type Morrey spaces.

Guliyev, Emin, Eroglu, Ahmet, Mammadov, Yagub (2010)

Abstract and Applied Analysis

Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class

Yanbo Ren, Shuang Ding (2022)

Czechoslovak Mathematical Journal

We collect known and prove new necessary and sufficient conditions for the weighted weak type maximal inequality of the form $Φ_{1} (λ) ϱ ({x \in X : M_{μ} f (x) > λ}) \leq c \int_{X} Φ_{2} (c | f (x) |) σ (x) d μ (x),$ which extends some known results.

Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I.

Gogatishvili, A., Kokilashvili, V. (1995)

Georgian Mathematical Journal

Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. II.

Gogatishvili, A., Kokilashvili, V. (1995)

Georgian Mathematical Journal

Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces

Aydin Sh. Shukurov (2012)

Colloquium Mathematicae

A necessary condition for Kostyuchenko type systems and system of powers to be a basis in $L_{p}$ (1 ≤ p < +∞) spaces is obtained. In particular, we find a necessary condition for a Kostyuchenko system to be a basis in $L_{p}$ (1 ≤ p < +∞).

New and old function spaces in the theory of PDEs and nonlinear analysis

Tadeusz Iwaniec, Carlo Sbordone (2004)

Banach Center Publications

New applications of Pták's extension theorem to weak compactness

Pedro José Paúl (1989)

Czechoslovak Mathematical Journal

New bounds for $A_{\infty}$ weights.

Radice, Teresa (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

New characterizations of some $L^{p}$ -spaces.

Jenkins, Russell S., Garimella, Ramesh V. (2000)

International Journal of Mathematics and Mathematical Sciences

New examples of K-monotone weighted Banach couples

Sergey V. Astashkin, Lech Maligranda, Konstantin E. Tikhomirov (2013)

Studia Mathematica

Some new examples of K-monotone couples of the type (X,X(w)), where X is a symmetric space on [0,1] and w is a weight on [0,1], are presented. Based on the property of w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X,X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is $t^{1 / p}$ for some p ∈ [1,∞], then $X = L_{p}$ . At...

New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]

P. N. Dowling, C. J. Lennard, B. Turett (2007)

Studia Mathematica

We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.

New inequalities for the jacobian

L. Greco, T. Iwaniec (1994)

Annales de l'I.H.P. Analyse non linéaire

Non interpolation in Morrey-Campanato and block spaces

Oscar Blasco, Alberto Ruiz, Luis Vega (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Nonaccessible filters in measure algebras and functionals on $L^{\infty} (λ) *$

Ryszard Frankiewicz, Grzegorz Plebanek (1994)

Studia Mathematica

Non-commutative interpolation of Sobolev-Besov and Lebesgue spaces with weights

Jutta Schmeisser (1981)

Czechoslovak Mathematical Journal

Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

Studia Mathematica

We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.

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