Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

The target is potential theory in connection with Morrey spaces on general metric measure spaces. The present paper is oritented to investigating Sobolev's inequality, Trudinger exponential integrability and continuity for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. A counterexample shows that our results are reasonable. In addition to the example above, what is new about this paper is that everything can be developed once the underlying measure does not charge any point.

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“…Our result contains the result of Trudinger [39] as well as those in [21,22,34]. For related results, see [2,[7][8][9][18][19][20]28,40].…”

Section: ( ) P(·)q(·) (X ·) Is Convex On [0 ∞) For Every X ∈ Xmentioning

confidence: 66%

“…7, we discuss the continuity of Riesz potentials of variable order, as an extension of [7,12,21,23]. For related results, see [8,19,20]. More precisely, in Sect.…”

Section: ( ) P(·)q(·) (X ·) Is Convex On [0 ∞) For Every X ∈ Xmentioning

confidence: 99%

Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents

Sawano

Shimomura

2013

Collect. Math.

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“…The operator I ρ was introduced in [19] and some partial results were announced in [18]. We refer to [16] for the boundedness of I ρ on Orlicz space L Φ (Ω) with bounded domain Ω ⊂ R n . See also [20,21,22,23] for the boundedness of I ρ on various spaces.…”

Section: Introductionmentioning

confidence: 99%

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

et al. 2018

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In the present paper, we will characterize the boundedness of the generalized fractional integral operators I ρ and the generalized fractional maximal operators M ρ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators M ρ and I ρ on generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators M ρ and I ρ on generalized Orlicz-Morrey spaces.

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“…For other examples, see [21]. See also [18] for the boundedness of I ρ on Orlicz space L Φ (Ω) with bounded domain Ω ⊂ R n .…”

Section: Resultsmentioning

confidence: 99%

Generalized Fractional Integral Operators and Their Commutators with Functions in Generalized Campanato Spaces on Orlicz Spaces

Shi¹,

Arai²,

Nakai³

2019

Taiwanese J. Math.

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We investigate the commutators [b, I ρ ] of generalized fractional integral operators I ρ with functions b in generalized Campanato spaces and give a necessary and sufficient condition for the boundedness of the commutators on Orlicz spaces. To do this we define Orlicz spaces with generalized Young functions and prove the boundedness of generalized fractional maximal operators on the Orlicz spaces.2010 Mathematics Subject Classification. 46E30, 42B35.

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Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

Cited by 48 publications

References 17 publications

Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents

Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

Generalized Fractional Integral Operators and Their Commutators with Functions in Generalized Campanato Spaces on Orlicz Spaces

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