scholarly journals On boundedness of operators of weak type $(\varphi_0, \psi_0, \varphi_1, \psi_1)$ in Lorentz spaces in limit cases

2021 ◽  
Vol 15 ◽  
pp. 107
Author(s):  
B.I. Peleshenko
Keyword(s):  
Lorentz Space ◽  
Weak Type ◽  
Lorentz Spaces

We prove theorems on boundedness of operators of weak type $(\varphi_0, \psi_0, \varphi_1, \psi_1)$ from Lorentz space $\Lambda_{\varphi,a}(\mathbb{R}^n)$ to $\Lambda_{\varphi,b}(\mathbb{R}^n)$ in “limit” cases, when one of functions $\varphi(t) / \varphi_0(t)$, $\varphi(t) / \varphi_1(t)$ slowly changes at zero and at infinity.

scholarly journals On interpolation of operators of weak type $$$(\phi_0, \psi_0, \phi_1, \psi_1)$$$ in Lorentz spaces in borderline cases

2018 ◽  
Vol 26 (1) ◽  
pp. 68
Author(s):  
B.I. Peleshenko ◽  
T.N. Semirenko
Keyword(s):  
Convex Functions ◽  
Lorentz Space ◽  
Weak Type ◽  
Lorentz Spaces ◽  
Slowly Varying Function ◽  
Borderline Cases ◽  
Interpolation Of Operators

The quaslinear operators of weak type $$$(\phi_0, \psi_0, \phi_1, \psi_1)$$$, analogs of the Calderon, Bennett operators in the case of concave and convex functions $$$\phi_0(t)$$$, $$$\psi_0(t)$$$, $$$\phi_1(t)$$$, $$$\psi_1(t)$$$ are considered. The theorems of interpolation of these operators from the Lorentz space $$$\Lambda_{\psi, b}(\mathbb{R}^n)$$$ into the space $$$\Lambda_{\psi, a}(\mathbb{R}^n)$$$ in cases when $$$0 < b \leqslant a \leqslant 1$$$ and relation of function $$$\phi^{\frac{1}{b}}(t)$$$ to one of functions $$$\phi_1(t)$$$, $$$\phi_2(t)$$$ is slowly varying function are proved.

Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces

2016 ◽  
Vol 22 (6) ◽  
pp. 1431-1439 ◽  
Author(s):  
Elona Agora ◽  
Jorge Antezana ◽  
María J. Carro
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Lorentz Spaces ◽  
Weighted Lorentz Spaces ◽  
Littlewood Maximal Operator

Weak-type inequalities for maximal operators acting on Lorentz spaces

2014 ◽  
Vol 101 ◽  
pp. 145-162
Author(s):  
Adam Osękowski
Keyword(s):  
Weak Type ◽  
Lorentz Spaces ◽  
Maximal Operators

SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

2010 ◽  
Vol 88 (1) ◽  
pp. 19-27 ◽  
Author(s):  
SORINA BARZA ◽  
JAVIER SORIA
Keyword(s):  
Lorentz Space ◽  
Lorentz Spaces ◽  
Best Constants ◽  
Sharp Constants ◽  
Dual Norm ◽  
Equivalent Norms ◽  
Weighted Lorentz Spaces ◽  
Weighted Lorentz Space

AbstractFor an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

Lorentz spaces of weak-type

1998 ◽  
Vol 49 (193) ◽  
pp. 93-103 ◽  
Author(s):  
J Soria
Keyword(s):  
Weak Type ◽  
Lorentz Spaces

scholarly journals The uniform Kadec-Klee property for the Lorentz spaces Lw,1

1996 ◽  
Vol 60 (1) ◽  
pp. 7-17 ◽  
Author(s):  
S. J. Dilworth ◽  
Yu-Ping Hsu
Keyword(s):  
Lorentz Space ◽  
Lorentz Spaces ◽  
Weak Star

AbstractIn this paper we show that the Lorentz space Lw, 1(0, ∞) has the weak-star uniform Kadec-Klee property if and only if inft>0 (w(αt)/w(t)) > 1 and supt>0(φ(αt) / φ(t))< 1 for all α ∈ (0, 1), where φ(t) = ∫t0 w(s) ds.

scholarly journals On the solid hull of the Hardy-Lorentz space

2009 ◽  
Vol 85 (99) ◽  
pp. 55-61 ◽  
Author(s):  
Miroljub Jevtic ◽  
Miroslav Pavlovic
Keyword(s):  
Lorentz Space ◽  
Lorentz Spaces ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Norm Space ◽  
Solid Hull

The solid hulls of the Hardy-Lorentz spaces Hp,q,0 < p < 1, 0 < q ? ? and Hp,? 0, 0 < p < 1, as well as of the mixed norm space H p,?,? 0,0 < p ? 1, 0 < ? < ?, are determined.

scholarly journals Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels

1994 ◽  
Vol 1 (1) ◽  
pp. 9-29
Author(s):  
I. Genebashvili ◽  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Weak Type ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Integral Transforms ◽  
Lorentz Spaces ◽  
Quasiconvex Functions ◽  
Homogeneous Type ◽  
Necessary And Sufficient ◽  
Positive Kernels ◽  
Homogeneous Type Space

Abstract Necessary and sufficient conditions are derived in order that an inequality of the form be fulfilled for some positive c independent of λ and a ν-measurable nonnegative function ƒ : X → R 1, where k : X × X × [0, ∞) → R 1 is a nonnegative measurable kernel, (X, d, μ) is a homogeneous type space, φη and ψ are quasiconvex functions, ψ ∈ Δ2, and t –α θ(t) is a decreasing function for some α, 0 < α < 1. A similar problem was solved in Lorentz spaces with weights.

scholarly journals Intrinsic Square Function Characterizations of Variable Hardy–Lorentz Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Khedoudj Saibi
Keyword(s):  
Measurable Function ◽  
Lorentz Space ◽  
Hölder Continuity ◽  
Continuity Condition ◽  
Lorentz Spaces ◽  
Square Function ◽  
Holder Continuity ◽  
Area Function ◽  
Intrinsic Square Function ◽  
Lusin Area Function

The aim of this paper is to establish the intrinsic square function characterizations in terms of the intrinsic Littlewood–Paley g-function, the intrinsic Lusin area function, and the intrinsic gλ∗-function of the variable Hardy–Lorentz space Hp⋅,qℝn, for p⋅ being a measurable function on ℝn satisfying 0<p−≔ess infx∈ℝnpx≤ess supx∈ℝnpx≕p+<∞ and the globally log-Hölder continuity condition and q∈0,∞, via its atomic and Littlewood–Paley function characterizations.

Interpolation of operators of weak type (ϕ0, ψ0, ϕ1, ψ1) in Lorentz spaces

2005 ◽  
Vol 57 (11) ◽  
pp. 1741-1762 ◽  
Author(s):  
B. I. Peleshenko
Keyword(s):  
Weak Type ◽  
Lorentz Spaces ◽  
Interpolation Of Operators
Sign in / Sign up

Export Citation Format

Share Document