Variable Lebesgue norm estimates for BMO functions. II

The paper concerns characterization of BMO in terms of Banach function spaces. In particular, we are interested in characterizing BMO by using the variable Lebesgue norm.     

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

Positivity - In the present paper, we will characterize the boundedness of the generalized fractional integral operators $$I_{\rho }$$ and the generalized fractional maximal operators $$M_{\rho }$$...     

A new Brézis‐Gallouët‐Wainger inequality from the viewpoint of the real interpolation functors

The Brézis‐Gallouët‐Wainger inequality describes a subtle embedding property into . The relation between the Brézis‐Gallouët‐Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between and the logarithmic boundedness, which is supposed to be the right‐hand side of the Brézis‐Gallouët‐Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem.     

Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces

The aim of this paper is to define the Besov–Morrey spaces and the Triebel– Lizorkin–Morrey spaces and to present a decomposition of functions belonging to these spaces. Our results contain an answer to the conjecture proposed by Mazzucato. The first author is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The second author is supported by Fūjyukai foundation and the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.     

The three-dimensional structure of aspergilloglutamic peptidase from Aspergillus niger

Aspergilloglutamic peptidase from Aspergillus niger is a novel pepstatin-insensitive acid endopeptidase distinct from the well-studied aspartic peptidases, and thus is an interesting target for protein structure/function studies. In the present study, we have determined the three-dimensional structure of the enzyme by X-ray crystallography to a 1.4-Å resolution. The results revealed that the enzyme has a unique structure, composed of two seven-stranded anti-parallel β-sheets which form a β-sandwich structure and appear to have a partial two-fold symmetry, suggesting its possible evolution by gene duplication and that the glutamic acid-110 and glutamine-24 in the heavy chain form a catalytic dyad, consistent with our results obtained by site-directed mutagenesis.     

Complex interpolation of various subspaces of Morrey spaces

In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano(2017) and Hakim et al.(2017).     

A predual of a predual of B_σ and its applications to commutators

A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.