Applications Of Orlicz Spaces

By Z. Ren, M. Rao. 2002

423 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bd6622652da2731df74423b8feb74f8fa6188ea5

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In Mathematical Physics

Citations in the corpus

Gradient estimates in Orlicz space for nonlinear elliptic equations (2008, background): “The theory of Orlicz spaces plays a crucial role in a very wide spectrum (see [21]).”
Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, background): “Recall that a function Φ : [0,∞) → [0,∞) is called an Orlicz function if it is nondecreasing, Φ(0) = 0, Φ(t) > 0 for t ∈ (0,∞) and limt→∞Φ(t) = ∞ (see, for example, [41, 44, 45]).”
Approximation Results for a General Class of Kantorovich Type Operators (2014, background): “For more information on Orlicz spaces and related topics, the reader can be addressed to [27, 29, 31, 32, 10].”
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, neutral): “Growth functions Recall that a function Φ : [0,∞) → [0,∞) is called an Orlicz function if it is nondecreasing, Φ(0) = 0, Φ(t) > 0 for t ∈ (0,∞) and limt→∞ Φ(t) = ∞ (see, for example, [59, 62, 63]).”
Fully anisotropic elliptic problems with minimally integrable data (2019, methodology): “An account of more recent developments can be found in [51,52].”
New real-variable characterizations of Musielak-Orlicz Hardy spaces (2012, neutral): “Growth functions Recall that a function Φ : [0, ∞) → [0, ∞) is called an Orlicz function if it is nondecreasing, Φ(0) = 0, Φ(t) > 0 for t ∈ (0, ∞) and limt→∞ Φ(t) = ∞ (see, for example, [20,32,33]).”
Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces (2015, background): “For further results concerning Orlicz spaces see [12, 40, 41, 43, 45, 46, 51].”
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “Since then, the theory of Orlicz spaces and its applications have been well developed (see, for example, [30, 31, 26]).”
Stochastic generalized porous media and fast diffusion equations (2006, neutral): “†The corresponding author: wangfy@bnu.edu.cn”
Non-monotone stochastic generalized porous media equations☆ (2008, background): “First, however, we need to introduce auxiliary spaces V and V ∗: It is easy to see that N(s) := ∫ r2 r1 |s|ν(dr), s ∈ R, is a ∆2-regular Young function so that the corresponding Orlicz space LN(m) is a reflexive separable Banach space (see [14]).”
Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, background): “Since then, the theory of the Orlicz spaces themselves has been well developed and the spaces have been widely used in probability, statistics, potential theory, partial differential equations, as well as harmonic analysis and some other fields of analysis; see, for example, [24, 25].”