Grand Orlicz spaces and global integrability of the Jacobian

Capone, Claudia; Fiorenza, Alberto; Karadzhov, Georgi E.

doi:10.7146/math.scand.a-15055

Cited by 11 publications

(11 citation statements)

References 12 publications

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“…On the other hand, they turned out to be useful also in other fields of Analysis (see [27] and references therein), in PDEs, in order to obtain the existence and uniqueness of the solution of a certain nonlinear equation in divergence form with right-hand side in L 1 (see e.g. [18]), and, finally, they were considered in interpolationextrapolation theory (see [5,13]). …”

Section: Notation and Preliminary Resultsmentioning

confidence: 99%

Some estimates in GΓ(p,m,w) spaces

Fiorenza

Rakotoson

2008

Journal of Mathematical Analysis and Applications

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We consider a class of rearrangement invariant Banach Function Spaces recently appeared in a paper by the same authors, containing at the same time some Lorentz spaces Γ (ν), classical Lebesgue spaces and small Lebesgue spaces. We discuss the main properties coming directly from the norm, and, for certain values of the involved parameters, we prove some estimates of the norm of the associate space.

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Section: Notation and Preliminary Resultsmentioning

confidence: 99%

Some estimates in GΓ(p,m,w) spaces

Fiorenza

Rakotoson

2008

Journal of Mathematical Analysis and Applications

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“…Lemma 1. Let 1 < p < ∞ and γ satisfy condition (3). Then there exists such a σ ∈ (0, p − 1) that Proof makes use of Lemma 1.…”

Section: Sufficiency Of Condition (3) For the Boundedness In The Spacmentioning

confidence: 97%

“…In the theory in PDE, it turns out that they are right spaces in which some nonlinear equations have to be considered. We refer for instance, to papers [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13].…”

Section: Introduction: Grand Lebesgue Spacesmentioning

confidence: 99%

Boundedness of Weighted Singular Integral Operators on a Carleson Curve in Grand Lebesgue Spaces

Kokilashvili¹

2010

AIP Conference Proceedings

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Symmetry of extremals of functional inequalities via spectral estimates for linear operators J. Math. Phys. 53, 095204 (2012) On the structure of positive maps: Finite-dimensional case J. Math. Phys. 53, 023515 (2012) Eigenfunctions decay for magnetic pseudodifferential operators J. Math. Phys. 52, 093709 (2011) An estimate for the resolvent of a non-self-adjoint differential operator on the half-line J. Math. Phys. 52, 043515 (2011) Additional information on AIP Conf. Proc.Abstract. We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set where the functions are defined is a Carleson curve in the complex plane. Note that weighted boundedness of an operator in grand Lebesgue space is known to be not the same as the boundedness in weighted grand Lebesgue space.

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“…where M is the Hardy-Littlewood maximal operator defined on X, i.e., We denote by [w] A1 the best possible constant in (4).…”

Section: Introductionmentioning

confidence: 99%

Extrapolation in weighted classical and grand Lorentz spaces. Application to the boundedness of integral operators

Kokilashvili

Meskhi

2020

Banach J. Math. Anal.

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We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal ones. PreliminariesLet (X, d, µ) be a quasi-metric measure space with a quasi-metric d and measure µ. A quasi-metric d is a function d : X × X → [0, ∞) which satisfies the following conditions: (i) d(x, y) = 0 if and only if x = y;(ii) for all x, y ∈ X, d(x, y) = d(y, x); 2010Mathematics Subject Classification: 46E30; 42B20; 42B25.

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Grand Orlicz spaces and global integrability of the Jacobian

Abstract: We introduce and investigate the grand Orlicz spaces and the grand Lorentz-Orlicz spaces. An application to the problem of global integrability of the Jacobian of orientation preserving mappings is given.

Cited by 11 publications

References 12 publications

Some estimates in GΓ(p,m,w) spaces

Some estimates in GΓ(p,m,w) spaces

Boundedness of Weighted Singular Integral Operators on a Carleson Curve in Grand Lebesgue Spaces

Extrapolation in weighted classical and grand Lorentz spaces. Application to the boundedness of integral operators

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