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1.
26 p, 395.3 KB Functional properties of rearrangement invariant spaces defined in terms of oscillations / Carro, María J. (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Gogatishvili, Amiran (Czech Academy of Sciences. Mathematical Institute) ; Martín i Pedret, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pick, Luboš (Charles University. Department of Mathematical Analysis)
Function spaces whose definition involves the quantity f** - f*, which measures the oscillation of f*, have recently attracted plenty of interest and proved to have many applications in various, quite diverse fields. [...]
2005 - 10.1016/j.jfa.2005.06.012
Journal of Functional Analysis, Vol. 229, Issue 2 (December 2005) , p. 375-404  
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2.
28 p, 260.1 KB Reduction theorems for operators on the cones of monotone functions / Gogatishvili, A. ; Stepanov, V. D. (Vladimir Dmitrievich) ; Centre de Recerca Matemàtica
For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. [...]
Centre de Recerca Matemàtica 2011 (Prepublicacions del Centre de Recerca Matemàtica ; 1067)  
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3.
21 p, 247.2 KB New pre-dual space of Morrey space / Gogatishvili, A. ; Mustafayev, R. Ch. ; Centre de Recerca Matemàtica
In this paper we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. [...]
Centre de Recerca Matemàtica 2011 (Prepublicacions del Centre de Recerca Matemàtica ; 1048)  
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4.
48 p, 324.5 KB Discretization and anti-discretization of rearrangement-invariant norms / Gogatishvili, Amiran ; Pick, Luboš
We develop a new method of discretization and anti-discretization of weighted inequalities which we apply to norms in classical Lorentz spaces and to spaces endowed with the so-called Hilbert norm. Main applications of our results include new integral conditions characterizing embeddings Γp(v) → Γq(w) and Γp(v) → Λq(w) and an integral characterization of the associate space to Γp(v), where p, q ∈ (0, ∞), v, w are weights on [0, ∞) and fΛp(v) = ∞ 0 f∗(t) pv(t) dt1/p, fΓp(v) = ∞ 0 f∗∗(t) pv(t) dt1/p.
2003 - 10.5565/PUBLMAT_47203_02
Publicacions matemàtiques, V. 47 N. 2 (2003) , p. 311-358  
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