Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen

By Z. W. Birnbaum, W. Orlicz. 1931

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Citations in the corpus

Geometric Lower Bounds for Distributed Parameter Estimation Under Communication Constraints (2018, background): “Recall that the ψ2-norm of a random variable X is defined by ‖X‖ψ2(P ) = inf{a > 0 : EP [exp( X2 a2 )] ≤ 2}, which is the Orlicz norm ofX associated with the Orlicz function ψ2(x) = exp(x 2)−1 Birnbaum and Orlicz (1931). There are also some equivalent definitions of ψ2-norm, and ‖X‖ψ2 ≤ σ if and onl”
Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, background): “On the other hand, as another generalization of L(R), the Orlicz space was introduced by Birnbaum–Orlicz in [4] and Orlicz in [23].”
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “On the other hand, due to the request of applications, as a natural extension of Lebesgue spaces, the Orlicz space was introduced by Birnbaum-Orlicz in [1] and Orlicz in [28].”
Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, background): “[3] and Orlicz in [43], which is widely used in various branches of analysis (see, for example, [44, 45, 1, 9, 26, 27, 55, 29, 30, 31] and their references).”
BOUNDEDNESS OF MULTILINEAR COMMUTATORS OF CALDERÓN-ZYGMUND OPERATORS ON ORLICZ SPACES OVER NON-HOMOGENEOUS SPACES (2012, methodology): “As a generalization of Lp(Rd), the Orlicz space was originally introduced by Birnbaum-Orlicz in [1] and Orlicz in [18].”
Musielak-Orlicz Campanato Spaces and Applications (2013, background): “On the other hand, as a generalization of Lp(Rn), the Orlicz space was introduced by Birnbaum-Orlicz [2] and Orlicz [33].”
New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, background): “On the other hand, as another generalization of L(R), the Orlicz spaces were introduced by Birnbaum–Orlicz in [3] and Orlicz in [48], 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, part”
Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, methodology): “These spaces were introduced by Birnbaum-Orlicz [3] and Orlicz [34], and widely used in the study of harmonic analysis as well as partial differential equations; see, for example, [1, 2, 6, 7, 8, 11, 12, 13, 14, 20, 30, 43, 48, 50].”
New real-variable characterizations of Musielak-Orlicz Hardy spaces (2012, background): “1 Introduction As the generalization of Lp(Rn), the Orlicz space was introduced by Birnbaum-Orlicz in [4] and Orlicz in [30].”
NORM-ONE PROJECTIONS IN BANACH SPACES (2001, methodology): “There are many monographs devoted to Orlicz spaces (see e.g. [KrRu61, RaRe91, Che96]).”
New Orlicz–Hardy spaces associated with divergence form elliptic operators (2009, background): “On the other hand, as another generalization of Lp(Rn), the Orlicz space was introduced by Birnbaum-Orlicz in [8] and Orlicz in [33], 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, part”
Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “On the other hand, as a natural generalization of Lp(Rn), the Orlicz space was introduced by Birnbaum-Orlicz in [9] and Orlicz in [77], which has extensive applications in several branches of mathematics (see, for example, [79, 80, 71, 55, 48] for more details).”
Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “Spaces of variable integrability can be traced back to Birnbaum-Orlicz [10], Orlicz [58] and Nakano [54, 55].”