Maximal and Potential Operators in Variable Exponent Morrey Spaces

By Alexandre Almeida, J. Hasanov, S. Samko. 2008

220 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/150bd6965335481f37ea0eec2f621628ab613c76

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. S. Samko
3. Kwok-Pun Ho
4. V. Kokilashvili
5. E. Nakai
6. P. Hasto
7. A. Meskhi
8. Dachun Yang

In Mathematical Physics

1. Yoshihiro Sawano
2. S. Samko
3. Kwok-Pun Ho
4. V. Kokilashvili
5. E. Nakai
6. A. Meskhi
7. Dachun Yang
8. Mitsuo Izuki

Citations in the corpus

• Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure (2010, methodology): “For some properties of the spaces M pð Þ qð Þ ð Þ, where is a bounded domain in R , we refer to [30] (see also [29] for variable exponent Morrey spaces defined on an SHT).”
• Local-to-global results in variable exponent spaces (2009, background): “Variable exponent Morrey spaces have been studied in [5, 32].”
• Fractional integration and differentiation of variable order: an overview (2012, methodology): “We also refer to the study of variable order fractional integrals in variable exponent Morrey spaces in [1, 15, 16, 27].”
• Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces (2010, methodology): “In [2] there was proved the boundedness of the maximal operator in variable exponent Morrey spaces L p(·),λ(·)( ) under the log-condition on p(·) and λ(·) and for potential operators, under the same log-condition and the assumptions infx∈ α(x) > 0,”
• Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, methodology): “For the rest of this paper, we use the lifting principle to introduce and study some new Morrey type spaces related to several Banach function spaces appeared in [4, 5, 20, 24, 25, 26, 32, 35, 41, 42, 43, 44, 47, 52, 56, 66, 67, 71, 73, 74, 75].”
• Morrey-Campanato Spaces: an Overview (2013, background): “Samko [6] (2008) the space Lp(⋅),λ(⋅)(Ω) was introduced as the space of functions with the finite norm”
• Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents (2011, background): “For further related results, we refer the reader to the papers [3, 16, 17].”
• Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent (2008, background): “The following statement holds (for Euclidean spaces see [ 2 ], Lemma 7). Proposition 1.3.”
• FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “Or equivalently, a function θ : R × (0,∞) → (0,∞) is said to satisfy the doubling condition if θ(·1, t·2) ∼ θ for all t ∈ [1, 2].”
• Boundedness of maximal operators and Sobolevʼs inequality on Musielak–Orlicz–Morrey spaces (2013, background): “In [3] and [12], Riesz kernel of variable order is also considered.”