scholarly journals An Optimal Interpolation Theorem of Marcinkiewicz Type in Orlicz Spaces

1998 ◽  
Vol 153 (2) ◽  
pp. 357-381 ◽  
Author(s):  
Andrea Cianchi
Keyword(s):  
Orlicz Spaces ◽  
Interpolation Theorem ◽  
Optimal Interpolation

scholarly journals A sharp form of the Marcinkiewicz interpolation theorem for Orlicz spaces

2020 ◽  
Vol 255 (2) ◽  
pp. 109-158
Author(s):  
Ron Kerman ◽  
Rama Rawat ◽  
Rajesh K. Singh
Keyword(s):  
Orlicz Spaces ◽  
Interpolation Theorem ◽  
Sharp Form ◽  
Marcinkiewicz Interpolation Theorem

scholarly journals New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation

2006 ◽  
Vol 4 (3) ◽  
pp. 275-304 ◽  
Author(s):  
Evgeniy Pustylnik ◽  
Teresa Signes
Keyword(s):  
Weak Type ◽  
Interpolation Theorem ◽  
Optimal Interpolation ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Type Interpolation ◽  
Rearrangement Invariant Spaces ◽  
Invariant Spaces ◽  
Quasiconcave Function

We study weak type interpolation for ultrasymmetric spacesL?,Ei.e., having the norm??(t)f*(t)?E˜, where?(t)is any quasiconcave function andE˜is arbitrary rearrangement-invariant space with respect to the measuredt/t. When spacesL?,Eare not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. In this paper we find better interpolation results, involving new types of rearrangement-invariant spaces,A?,b,EandB?,b,E, which are described and investigated in detail.

Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

2020 ◽  
Vol 72 (2) ◽  
pp. 235-259
Author(s):  
Lech Maligranda ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integrals ◽  
Orlicz Spaces

Martingale Rransforms between Hardy-Orlicz Spaces of LΦPredictable Martingales

2012 ◽  
Vol 14 (3) ◽  
pp. 245
Author(s):  
Feng LUO ◽  
Lin YU ◽  
Hongping GUO
Keyword(s):  
Orlicz Spaces

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

scholarly journals New Gridded Product for the Total Columnar Atmospheric Water Vapor over Ocean Surface Constructed from Microwave Radiometer Satellite Data

2021 ◽  
Vol 13 (12) ◽  
pp. 2402
Author(s):  
Weifu Sun ◽  
Jin Wang ◽  
Yuheng Li ◽  
Junmin Meng ◽  
Yujia Zhao ◽  
...  
Keyword(s):  
Water Vapor ◽  
Microwave Radiometer ◽  
Atmospheric Water Vapor ◽  
Global Ocean ◽  
Optimal Interpolation ◽  
Fusion Product ◽  
Mean Deviation ◽  
Atmospheric Water ◽  
Absolute Deviation ◽  
Better Than

Based on the optimal interpolation (OI) algorithm, a daily fusion product of high-resolution global ocean columnar atmospheric water vapor with a resolution of 0.25° was generated in this study from multisource remote sensing observations. The product covers the period from 2003 to 2018, and the data represent a fusion of microwave radiometer observations, including those from the Special Sensor Microwave Imager Sounder (SSMIS), WindSat, Advanced Microwave Scanning Radiometer for Earth Observing System sensor (AMSR-E), Advanced Microwave Scanning Radiometer 2 (AMSR2), and HY-2A microwave radiometer (MR). The accuracy of this water vapor fusion product was validated using radiosonde water vapor observations. The comparative results show that the overall mean deviation (Bias) is smaller than 0.6 mm; the root mean square error (RMSE) and standard deviation (SD) are better than 3 mm, and the mean absolute deviation (MAD) and correlation coefficient (R) are better than 2 mm and 0.98, respectively.

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