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Variable Exponent Lebesgue Spaces
, 2013
"... p: Ω ⊆ Rd → [1,∞] measurable is called exponent. p+: = ess supx∈Ω p(x) p −: = ess infx∈Ω p(x) For measurable f define the modular %p(·)(f):= ..."
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p: Ω ⊆ Rd → [1,∞] measurable is called exponent. p+: = ess supx∈Ω p(x) p −: = ess infx∈Ω p(x) For measurable f define the modular %p(·)(f):=
KOLMOGOROV COMPACTNESS CRITERION IN VARIABLE EXPONENT LEBESGUE SPACES
, 903
"... Abstract. The wellknown Kolmogorov compactness criterion is extended to the case of variable exponent Lebesgue spaces Lp(·) (Ω), where Ω is a bounded open set in Rn and p(·) satisfies some “standard” conditions. Our final result should be called KolmogorovTulajkovSudakov compactness criterion, si ..."
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Abstract. The wellknown Kolmogorov compactness criterion is extended to the case of variable exponent Lebesgue spaces Lp(·) (Ω), where Ω is a bounded open set in Rn and p(·) satisfies some “standard” conditions. Our final result should be called KolmogorovTulajkovSudakov compactness criterion
Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces
"... By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weaktype inequality on variable exponent Lebesgue spaces. ..."
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By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weaktype inequality on variable exponent Lebesgue spaces.
ON CONVERSE THEOREMS OF TRIGONOMETRIC APPROXIMATION IN WEIGHTED VARIABLE EXPONENT LEBESGUE SPACES
"... Abstract. In this work we prove improved converse theorems of trigonometric approximation in variable exponent Lebesgue spaces with some Muckenhoupt weights. ..."
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Abstract. In this work we prove improved converse theorems of trigonometric approximation in variable exponent Lebesgue spaces with some Muckenhoupt weights.
Open problems in variable exponent Lebesgue and Sobolev spaces
 IN: ”FUNCTION SPACES, DIFFERENTIAL OPERATORS AND NONLINEAR ANALYSIS”, PROC. CONFERENCE HELD IN MILOVY, BOHEMIANMORAVIAN UPLANDS, MAY 28JUNE 2, 2004, MATH. INST. ACAD. SCI. CZECH
, 2005
"... In this article we provide an overview of several open problems in variable exponent spaces. The problems are related to boundedness of the maximal operator, interpolation theory, density of smooth functions and Sobolev embeddings. We also extend a result on complex interpolation to the variable e ..."
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Cited by 68 (4 self)
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In this article we provide an overview of several open problems in variable exponent spaces. The problems are related to boundedness of the maximal operator, interpolation theory, density of smooth functions and Sobolev embeddings. We also extend a result on complex interpolation to the variable
Lipschitz Estimates for Fractional Multilinear Singular Integral on Variable Exponent Lebesgue Spaces
"... We obtain the Lipschitz boundedness for a class of fractional multilinear operators with rough kernels on variable exponent Lebesgue spaces. Our results generalize the related conclusions on Lebesgue spaces with constant exponent. ..."
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We obtain the Lipschitz boundedness for a class of fractional multilinear operators with rough kernels on variable exponent Lebesgue spaces. Our results generalize the related conclusions on Lebesgue spaces with constant exponent.
Variable exponent Lebesgue spaces on metric spaces: the HardyLittlewood maximal operator
, 2003
"... In this article we introduce variable exponent Lebesgue spaces on metric measure spaces and consider a central tool in geometric analysis: the HardyLittlewood maximal operator. We show that the maximal operator is bounded provided the variable exponent satises a logHölder type estimate. This con ..."
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Cited by 22 (5 self)
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In this article we introduce variable exponent Lebesgue spaces on metric measure spaces and consider a central tool in geometric analysis: the HardyLittlewood maximal operator. We show that the maximal operator is bounded provided the variable exponent satises a logHölder type estimate
Some Applications to Lebesgue Points in Variable Exponent Lebesgue Spaces
"... Özet. Dağılım parametreli sistemler için optimal kontrol teorisinde kullanışlı olan, Lebesgue regüler noktalarının bazı sonuçları ispatlanmıştır. Anahtar Kelimeler. Değişken üslu ̈ Lebesgue uzayı, regüler Lebesgue noktaları, optimal kontrol. Abstract. Some corollaries of Lebesgue’s regula ..."
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Özet. Dağılım parametreli sistemler için optimal kontrol teorisinde kullanışlı olan, Lebesgue regüler noktalarının bazı sonuçları ispatlanmıştır. Anahtar Kelimeler. Değişken üslu ̈ Lebesgue uzayı, regüler Lebesgue noktaları, optimal kontrol. Abstract. Some corollaries of Lebesgue’s
MAXIMAL OPERATOR IN VARIABLE EXPONENT LEBESGUE SPACES ON UNBOUNDED QUASIMETRIC MEASURE SPACES
"... We study the HardyLittlewood maximal operator M on Lp(·)(X) when X is an unbounded (quasi)metric measure space, and p may be unbounded. We consider both the doubling and general measure case, and use two versions of the logHölder condition. As a special case we obtain the criterion for a boundedne ..."
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We study the HardyLittlewood maximal operator M on Lp(·)(X) when X is an unbounded (quasi)metric measure space, and p may be unbounded. We consider both the doubling and general measure case, and use two versions of the logHölder condition. As a special case we obtain the criterion for a boundedness of M on Lp(·)(Rn, μ) for arbitrary, possibly nondoubling, Radon measures. 1.
Results 1  10
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