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Maximal and Potential Operators in Variable Exponent Morrey Spaces
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Alexandre Almeida
Published/Copyright:
March 10, 2010
Abstract
We prove the boundedness of the Hardy–Littlewood maximal operator on variable Morrey spaces 𝐿𝑝(·), λ(·)(Ω) over a bounded open set Ω ⊂ ℝ𝑛 and a Sobolev type 𝐿𝑝(·), λ(·) → 𝐿𝑞(·), λ(·)-theorem for potential operators 𝐼α(·), also of variable order. In the case of constant α, the limiting case is also studied when the potential operator 𝐼α acts into BMO space.
Key words and phrases:: Maximal function; fractional maximal operator; Riesz potential; Morrey space; variable exponent; Hardy–Littlewood–Sobolev type estimate; BMO space
Received: 2007-09-14
Published Online: 2010-03-10
Published in Print: 2008-June
© Heldermann Verlag
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Articles in the same Issue
- Maximal and Potential Operators in Variable Exponent Morrey Spaces
- On the Essential Norm for the Hilbert Transforms in 𝐿𝑝(𝑥) Spaces
- Turbulence of Real Functions
- An Analytic Proof of the Matrix Spectral Factorization Theorem
- On Estimating the Approximation of Locally Summable Functions by Gegenbauer Singular Integrals
- Sobolev Spaces with Muckenhoupt Weights, Singularities and Inequalities
- Wavelets and Modular Inequalities in Variable 𝐿𝑝 Spaces
- A New Approach to the Sawyer and Sinnamon Characterizations of Hardy's Inequality for Decreasing Functions
- A Note on Maximal Operator on 𝐿𝑝(𝑡) (Ω)Spaces
- On Absolutely Nonmeasurable Sets and Functions
- On Fractional Integrals on the Plane Curves of Finite Length
- Essential Spectrum and Exponential Decay Estimates of Solutions of Elliptic Systems of Partial Differential Equations. Applications to Schrödinger and Dirac Operators
- Compact Commutators on Morrey Spaces with Non-Doubling Measures
- The Boundedness of Maximal Functions in Orlicz–Campanato Spaces of Homogeneous Type
- Wavelet Bases in Lorentz and Zygmund Spaces
Keywords for this article
Maximal function;
fractional maximal operator;
Riesz potential;
Morrey space;
variable exponent;
Hardy–Littlewood–Sobolev type estimate;
BMO space
Articles in the same Issue
- Maximal and Potential Operators in Variable Exponent Morrey Spaces
- On the Essential Norm for the Hilbert Transforms in 𝐿𝑝(𝑥) Spaces
- Turbulence of Real Functions
- An Analytic Proof of the Matrix Spectral Factorization Theorem
- On Estimating the Approximation of Locally Summable Functions by Gegenbauer Singular Integrals
- Sobolev Spaces with Muckenhoupt Weights, Singularities and Inequalities
- Wavelets and Modular Inequalities in Variable 𝐿𝑝 Spaces
- A New Approach to the Sawyer and Sinnamon Characterizations of Hardy's Inequality for Decreasing Functions
- A Note on Maximal Operator on 𝐿𝑝(𝑡) (Ω)Spaces
- On Absolutely Nonmeasurable Sets and Functions
- On Fractional Integrals on the Plane Curves of Finite Length
- Essential Spectrum and Exponential Decay Estimates of Solutions of Elliptic Systems of Partial Differential Equations. Applications to Schrödinger and Dirac Operators
- Compact Commutators on Morrey Spaces with Non-Doubling Measures
- The Boundedness of Maximal Functions in Orlicz–Campanato Spaces of Homogeneous Type
- Wavelet Bases in Lorentz and Zygmund Spaces
