The Hardy–Littlewood Maximal Operator

By D. Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth. 2014

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2358f91e44678cd40584b3cd018d4e6f03ed187

How researchers see this paper

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

In Applied Mathematics

1. Yoshihiro Sawano
2. E. Nakai
3. Kwok-Pun Ho
4. S. Samko
5. P. Hasto
6. Dachun Yang
7. Shohei Nakamura
8. Wen Yuan

In Mathematical Physics

1. Yoshihiro Sawano
2. E. Nakai
3. Kwok-Pun Ho
4. Dachun Yang
5. S. Samko
6. Shohei Nakamura
7. Wen Yuan
8. Jiang-Hua Lu

Citations in the corpus

• Generalized Morrey spaces and trace operator (2016, unknown): “[39] Let 0 < q <∞ and φ : (0,∞) → (0,∞) be a function.”
• Progress in Mathematics (2013, methodology): “In the Euclidean space R this was shown by Nakai in [Nak94].”
• Generalized weighted Morrey spaces and classical operators (2016, methodology): “To explain the situation for the unweighted spaces, we refer to the works [18] and [9].”
• Compactness of Commutators for Singular Integrals on Morrey Spaces (2012, background): “Note that χB(x) ∼ 2 −kn when x ∈ 2B\2B and invoke the following fact (see [34]): for 0 < δ < 1, 0 < λ < n, and 1 < p < ∞, there is a C > 0 such that for any f ∈ L(R),”
• The singular integral operator and its commutator on weighted Morrey spaces (2016, background): “Kováčik and Rákosńık [21] have established that the generalized Lebesgue space L(R) with variable exponent p(·) is a Banach function space and its associate space is L ′(·)(Rn) with norm equivalence, where p′(·) denotes the conjugate exponent given by 1 p(·) + 1 p(·) = 1.”
• Morrey-Campanato Spaces: an Overview (2013, background): “Nakai [72] (1994) for X = R, and the spaces Lpψ(X) with the (quasi)norm (21) in J.”
• Boundedness of the Maximal and Singular Operators on Generalized Orlicz–Morrey Spaces (2013, methodology): “The following statement, containing results obtained in [13, 14, 15, 27, 30] was proved in [1] (see also [16]).”
• Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, background): “The variable exponent analysis recently gains a lot of attentions [4, 5, 14, 15, 17, 18, 19, 20, 21, 36, 41, 44, 49, 50, 57, 75] because the boundedness of several important linear operators in analysis, especially, the Hardy–Littlewood maximal operator, can be established for the variable Lebesgue ”
• 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].”
• The maximal operator on generalized Orlicz spaces (2015, methodology): “It was Diening [5] who opened the floodgate by proving the boundedness of the maximal operator under natural and essentially optimal conditions on the exponent (see also [4, 15, 18]).”
• Boundedness of maximal operators and Sobolevʼs inequality on Musielak–Orlicz–Morrey spaces (2013, methodology): “Adams [1] (also [5] and [19]): For 0 < α < N , 1 < p < N/α and 0 < λ < N − αp, ‖Iα ∗ f ‖q,λ C‖f ‖p,λ where 1 q = 1 p − α N − λ This result was extended to Orlicz–Morrey spaces and generalized to Riesz kernel by E.”
• Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel (2012, background): “In [17] the following statement was proved for the commutators of fractional integral operators with rough kernels, containing the result in [34, 36].”
• A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “In [56], Nakai established the boundedness of the Hardy-Littlewood maximal operator, singular integral (of Calderón-Zygmund type), and fractional integral operators on Morrey spaces with variable growth function φ(x, r).”
• A Thought on Generalized Morrey Spaces (2018, background): “In [76] Nakai defined the generalized Morrey space Mq (Rn) to be the set of all measurable functions f such that”
• Characterizations For The Generalized Fractional Integral Operators On Morrey Spaces (2014, methodology): “The work [35] is a passage from [25] to the metric measure space whose underlying measure does not satisfy the doubling condition.”
• Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces (2015, unknown): “The latter condition is quite unnatural, and it was subsequently improved to a metric decay condition in [4] and a more general integral decay condition in [18].”