Hardy spaces with variable exponents and generalized Campanato spaces

Let T be the singular integral operator with variable kernel de ned byand D γ ( ≤ γ ≤ ) be the fractional di erentiation operator. Let T * and T ♯ be the adjoint of T and the pseudo-adjoint of T, respectively. The aim of this paper is to establish some boundedness for TD γ − D γ T and via the convolution operator T m,j and Calderón-Zygmund operator, and then establish their boundedness on these spaces. The boundedness on HMKMoreover, the authors also establish various norm characterizations for the product T T and the pseudo-product T ○ T .

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“…We refer the reader to [28][29][30] for details on the classical Hardy spaces. The variable exponent case is shown in [22] by Nakai and Sawano. …”

Section: De Nition 23 ([26]) Letmentioning

confidence: 99%

Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents

Yang

Tao

2018

Open Mathematics

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“…We shall also show the L Φ -version of Kerman-Sawyer inequality. Using the vector-valued inequality, in Section 7 we shall establish a decomposition result for functions in Musielak-Orlicz spaces as an extension of [23] and [24] for the case of Lebesgue spaces with variable exponents and Orlicz spaces. See [4,13,14,26,27,37] for related results.…”

Section: Fumi-yuki Maeda Yoshihiro Sawano and Tetsu Shimomuramentioning

confidence: 99%

Some norm inequalities in Musielak-Orlicz spaces

Maeda¹,

Sawano

Shimomura

2016

Ann. Acad. Sci. Fenn. Math.

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“…We use ω to measure the continuity of functions. See [26] for the Lebesgue measure case. To prove Theorem 7.1, we need Lemmas 7.2 and 7.3.…”

Section: In This Casementioning

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 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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Hardy spaces with variable exponents and generalized Campanato spaces

Cited by 330 publications

References 16 publications

Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents

Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents

Some norm inequalities in Musielak-Orlicz spaces

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

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