MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT

By Lars Diening, Petteri Harjulehto, P. Hasto, Y. Mizuta, Tetsu Shimomura. 2009

126 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/10b4256e8a6f478c2ceffccd5b0ceca778f77b30

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Dachun Yang
2. Ciqiang Zhuo
3. Wen Yuan
4. H. Kempka
5. Yiyu Liang
6. P. Hasto
7. Petteri Harjulehto
8. Jan Vyb'iral

Citations in the corpus

• Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, unknown): “This result has been generalized to wider classes of exponents p(·) in [11, 40] and [15].”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, methodology): “But the modern development was started with the article [37] of Kováčik and Rákosńık in 1991 and widely used in the study of harmonic analysis as well as partial differential equations; see, for example, [6, 12, 13, 14, 17, 18, 19, 21, 32, 48].”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “The variable Lebesgue spaces have already widely used in the study of harmonic analysis; see, for example, [10, 9, 11, 14, 15, 48, 26].”
• Lorentz spaces with variable exponents (2012, background): “The study of the maximal operator in the frame of Lebesgue spaces with variable exponents attracted a lot of attention with the most important breakthroughs being achieved in [10, 8, 26, 12, 7].”
• ATOMIC DECOMPOSITION OF HARDY-MORREY SPACES WITH VARIABLE EXPONENTS (2015, background): “One of the important results in the variable exponent analysis is the identification of the class of exponent functions for which the Hardy–Littlewood maximal function is bounded on the corresponding Lebesgue spaces with variable exponent [10, 11, 13, 15, 16, 36, 38, 39, 47, 48, 49].”
• Function spaces of variable smoothness and integrability (2007, unknown): “Most recently, Diening, Harjulehto, Hästö, Mizuta &Shimomura [15] have studied Sobolev embeddings whenp→ 1 using Lebesgue spaces with anL logL-character on the lower end in place ofL1.”
• FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “(3) [20, 39] (2009): If a variable exponent p(·) : R → [1,∞] satisfies 1 < p− ≤ p+ ≤ ∞ and 1/p(·) ∈ LH(R), then the Hardy-Littlewood maximal operator M is bounded on Lp(·)(Rn).”
• 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].”
• Minimizers of the variable exponent, non-uniformly convex Dirichlet energy (2008, unknown): “Spaces with p = ∞ have been investigated in [16,18,43].”
• Sobolev inequalities with variable exponent attaining the values $1$ and $n$ (2008, background): “In some recent investigations it has been found that one needs to modify the scales of spaces at the end point to properly deal with such limiting phenomena, see [9], [17].”
• Monotone operator theory for unsteady problems in variable exponent spaces (2012, background): “The next result is of great importance for the theory of generalized Lebesgue spaces and can be found in this form in [14,31,32].”