Weak Type Inequalities for Fractional Integral Operators on Generalized Non-Homogeneous Morrey Spaces

Sihwaningrum, Idha

doi:10.4208/ata.2012.v28.n1.8

Cited by 9 publications

(12 citation statements)

References 13 publications

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“…The next lemma presents an inequality involving the modified Hardy-Littlewood maximal operator . This inequality is an important part of the proof of the weak type inequalities for in [16,19]. See [8] for similar results.…”

Section: Weak Type Inequalities For Via the Chebyshev Inequalitymentioning

confidence: 72%

“…Sihwaningrum et al [19] proved the weak type inequalities for on generalized nonhomogeneous Morrey space by assuming that satisfies the integral condition; that is, ∫ ∞ ( ( ) / ) ≤ ( ) for every > 0. In [19], the weak type inequalities for are also proved by using the weak type inequalities for . In this paper, we remove the integral condition of in the hypothesis of our proposition below.…”

Section: Weak Type Inequalities For Via a Hedberg Type Inequality Andmentioning

confidence: 99%

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Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

Gunawan

Hakim

Sawano

et al. 2013

Journal of Function Spaces and Applications

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We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

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Section: Weak Type Inequalities For Via the Chebyshev Inequalitymentioning

confidence: 72%

Section: Weak Type Inequalities For Via a Hedberg Type Inequality Andmentioning

confidence: 99%

Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

Gunawan

Hakim

Sawano

et al. 2013

Journal of Function Spaces and Applications

Self Cite

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“…Following the appearance of [28], there has been a significant interest in the study of this topic (cf. [17,26,39,40] and the references therein for the part of the recent developments in this direction).…”

Section: Introductionmentioning

confidence: 99%

On the solutions of Caputo–Hadamard Pettis-type fractional differential equations

Cichoń

Salem

2019

RACSAM

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Let E be a Banach space with the topological dual E *. The aim of this paper is twofold. On the one hand, we prove some basic properties of Hadamard-type fractional integral operators. These results are related to earlier results about integral operators acting on different function spaces, but for the vector-valued case they are of independent interest. Note that we discuss it in a rather general setting. We study Hadamard-Pettis integral operators in both single and multivalued case. On the other hand, we apply these results to obtain the existence of solutions of the fractional-type problem d α x(t) dt α = λ f (t, x(t)), α ∈ (0, 1), t ∈ [1, e], x(1) + bx(e) = h with certain constants λ, b, where h ∈ E and f : [1, e]× E → E is Pettis integrable function such that, for every ϕ ∈ E * , ϕ f lies in an appropriate Orlicz spaces. Here d α dt α stands the Caputo-Hadamard fractional differential operator.

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“…The work using the growth measure is initiated in [32,45]; and the later work can be found in [15,21,33,39,40,42,47]. For Gauss measure spaces, see [22].…”

Section: Introductionmentioning

confidence: 99%

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

Sihwaningrum

Gunawan

Nakai

2018

Mathematische Nachrichten

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We establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces (X,d,μ) without the assumption of the growth condition on μ. The results are generalization and improvement of some known results. We also give the vector‐valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of Hytönen.

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Weak Type Inequalities for Fractional Integral Operators on Generalized Non-Homogeneous Morrey Spaces

Abstract: We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].

Cited by 9 publications

References 13 publications

Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

On the solutions of Caputo–Hadamard Pettis-type fractional differential equations

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

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