Fractional integrals on Herz-Morrey spaces with variable exponent

Izuki, Mitsuo

doi:10.32917/hmj/1291818849

Cited by 63 publications

(34 citation statements)

References 7 publications

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“…Obviously,̇( ⋅),0 , (⋅) (ℝ ) =̇( ⋅) (⋅), (ℝ ). If (⋅) is a constant, theṅ( ⋅), , (⋅) (ℝ ) =̇, , (⋅) (ℝ ), which is defined first by Izuki [20]. If both (⋅) and (⋅) are constants, theṅ( ⋅), , (⋅) (ℝ ) conincides with the classical Morrey-Herz spaceṡ , , (ℝ ) defined in [25].…”

Section: Boundedness On Morrey-herz Spaces With Variable Exponentsmentioning

confidence: 96%

“…We note that if

p false(\cdot false) \in P false(R^{n} false)

, then

p false(\cdot false) \in B false(R^{n} false)

is equivalent to

p^{'} false(\cdot false) \in B false(R^{n} false)

, see ( see also [, Proposition 2]).…”

Section: Preliminaries and Lemmasmentioning

confidence: 99%

“…Remark Obviously,

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), 0} false(R^{n} false) = {\overset{K}{true}}_{p (\cdot), q}^{α (\cdot)} false(R^{n} false)

. If

α (\cdot)

is a constant, then

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), λ} false(R^{n} false) = M {\overset{K}{true}}_{q, p (\cdot)}^{α, λ} false(R^{n} false)

, which is defined first by Izuki . If both

α (\cdot)

and

p (\cdot)

are constants, then

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), λ} false(R^{n} false)

conincides with the classical Morrey–Herz spaces

M {\overset{K}{true}}_{p, q}^{α, λ} false(R^{n} false)

defined in .…”

Section: Boundedness On Morrey–herz Spaces With Variable Exponentsmentioning

confidence: 99%

See 2 more Smart Citations

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

Wang

Li-sheng

2018

Mathematische Nachrichten

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Section: Boundedness On Morrey-herz Spaces With Variable Exponentsmentioning

confidence: 96%

“…We note that if

p false(\cdot false) \in P false(R^{n} false)

, then

p false(\cdot false) \in B false(R^{n} false)

is equivalent to

p^{'} false(\cdot false) \in B false(R^{n} false)

, see ( see also [, Proposition 2]).…”

Section: Preliminaries and Lemmasmentioning

confidence: 99%

“…Remark Obviously,

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), 0} false(R^{n} false) = {\overset{K}{true}}_{p (\cdot), q}^{α (\cdot)} false(R^{n} false)

. If

α (\cdot)

is a constant, then

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), λ} false(R^{n} false) = M {\overset{K}{true}}_{q, p (\cdot)}^{α, λ} false(R^{n} false)

, which is defined first by Izuki . If both

α (\cdot)

and

p (\cdot)

are constants, then

M {\overset{K}{true}}_{q, p (\cdot)}^{α (\cdot), λ} false(R^{n} false)

conincides with the classical Morrey–Herz spaces

M {\overset{K}{true}}_{p, q}^{α, λ} false(R^{n} false)

defined in .…”

Section: Boundedness On Morrey–herz Spaces With Variable Exponentsmentioning

confidence: 99%

See 1 more Smart Citation

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

Wang

Li-sheng

2018

Mathematische Nachrichten

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“…Lemma 2.2 [12] If q(·) ∈ B(R n ), then there exist positive constants δ ∈ (0, 1) and C > 0 such that…”

Section: Next We Define the Herz-morrey Spaces With Variable Exponentmentioning

confidence: 99%

“…Let us explain the outline of this article. In Section 2 we state some important properties of L q(·) (R n ) based on [8,12,18,23], and give some lemmas which will be needed for proving our main theorem. In Section 3 we prove the boundedness of sublinear operators on Herz-Morrey spaces with variable exponent MK α,λ p,q(·) (R n ), and obtain the corresponding corollaries.…”

Section: Introductionmentioning

confidence: 99%

Boundedness of some sublinear operators on Herz–Morrey spaces with variable exponent

2014

Georgian Mathematical Journal

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Intrinsic square functions and commutators on Morrey‐Herz spaces with variable exponents

Abdalmonem

Scapellato

2021

Math Methods in App Sciences

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Fractional integrals on Herz-Morrey spaces with variable exponent

Cited by 63 publications

References 7 publications

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

Boundedness of some sublinear operators on Herz–Morrey spaces with variable exponent

Intrinsic square functions and commutators on Morrey‐Herz spaces with variable exponents

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