Orlicz–Morrey Spaces and Fractional Operators

By taking an interest in a natural extension to the small parameters of the trace inequality for Morrey spaces, Orlicz–Morrey spaces are introduced and some inequalities for generalized fractional integral operators on Orlicz–Morrey spaces are established. The local boundedness property of the Orlicz maximal operators is investigated and some Morrey-norm equivalences are also verified. The result obtained here sharpens the one in our earlier papers.     

Notes on the partition property of {\mathcal{P}_\kappa\lambda}

We investigate the partition property of ${\mathcal{P}_{\kappa}\lambda}$ . Main results of this paper are as follows: (1) If λ is the least cardinal greater than κ such that ${\mathcal{P}_{\kappa}\lambda}$ carries a (λ ^κ , 2)-distributive normal ideal without the partition property, then λ is ${\Pi^1_n}$ -indescribable for all n?<?ω but not ${\Pi^2_1}$ -indescribable. (2) If cf(λ) ≥?κ, then every ineffable subset of ${\mathcal{P}_{\kappa}\lambda}$ has the partition property. (3) If cf(λ) ≥ κ, then the completely ineffable ideal over ${\mathcal{P}_{\kappa}\lambda}$ has the partition property.     

Complex interpolation of Besov spaces and Triebel–Lizorkin spaces with variable exponents

This paper concerns the complex interpolation of Besov spaces and Triebel–Lizorkin spaces with variable exponents.     

New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets

In this paper, the authors establish new characterizations of the recently introduced Besov-type spaces $\dot{B}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ and Triebel-Lizorkin-type spaces $\dot{F}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ with p∈(0,∞], s∈?, τ∈[0,∞), and q∈(0,∞], as well as their preduals, the Besov-Hausdorff spaces $B\!\dot{H}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ and Triebel-Lizorkin-Hausdorff spaces $F\!\dot{H}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ , in terms of the local means, the Peetre maximal function of local means, and the tent space (the Lusin area function) in both discrete and continuous types. As applications, the authors then obtain interpretations as coorbits in the sense of Rauhut (Stud. Math. 180:237–253, 2007) and discretizations via biorthogonal wavelet bases for the full range of parameters of these function spaces. Even for some special cases of this setting such as $\dot{F}^{s}_{\infty,q}({\mathbb{R}}^{n})$ for s∈?, q∈(0,∞] (including ?BMO(? ⁿ ) when s=0 and q=2), the Q space Q _α (? ⁿ ), the Hardy-Hausdorff space HH _?α (? ⁿ ) for α∈(0,min{n/2,1}), the Morrey space ${\mathcal{M}}^{u}_{p}({\mathbb{R}}^{n})$ for 1<p≤u<∞, and the Triebel-Lizorkin-Morrey space $\dot{\mathcal{E}}^{s}_{upq}({\mathbb{R}}^{n})$ for 0<p≤u<∞, s∈? and q∈(0,∞], some of these results are new.     

Multilinear fractional integrals on Morrey spaces

In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.     

Nickel(II) and copper(II) complexes of β-unsubstituted 5,15-diazaporphyrins and pyridazine-fused diazacorrinoids: metal-template syntheses and peripheral functionalizations

The present paper reports the first comprehensive study on the synthesis, structures, optical and electrochemical properties, and peripheral functionalizations of nickel(II) and copper(II) complexes of β-unsubstituted 5,15-diazaporphyrins (M-DAP; M = Ni, Cu) and pyridazine-fused diazacorrinoids (Ni-DACX; X = N, O). These two classes of compounds were constructed starting from mesityldipyrromethane by a metal-template method. Ni-DAP and Cu-DAP were prepared in high yields by the reaction of the respective metal-bis(dibromodipyrrin) complexes with NaN(3)-CuX (X = I, Br), whereas Ni-DACN and Ni-DACO were formed as predominant products by the reaction with NaN(3). In both cases, the metal centers change their geometry from tetrahedral to square planar during the aza-annulation; X-ray crystallographic analyses of M-DAPs showed highly planar diazaporphyrin π planes. The Q band of Ni-DAP was redshifted and intensified compared with that of a nickel-porphyrin reference, due to the involvement of electronegative nitrogen atoms at the meso positions. It was found that the peripheral bromination of Ni-DAP and Ni-DACO occurred regioselectively to afford Ni-DAP-Br(4) and Ni-DACO-Br, respectively. These brominated derivatives underwent Stille reactions with tributyl(phenyl)stannane to give the corresponding phenylated derivatives, Ni-DAP-Ph(4) and Ni-DACO-Ph. On the basis of the absorption spectra and X-ray analysis, it has been concluded that the attached phenyl groups efficiently conjugate with the diazaporphyrin π system. The present results unambiguously corroborate that the β-unsubstituted DAPs and DACXs are promising platforms for the development of a new class of π-conjugated azaporphyrin-based materials.     

Preparation and photophysical and photoelectrochemical properties of a covalently fixed porphyrin-chemically converted graphene composite

Chemically converted graphene (CCG) covalently linked with porphyrins has been prepared by a Suzuki coupling reaction between iodophenyl-functionalized CCG and porphyrin boronic ester. The covalently linked CCG-porphyrin composite was designed to possess a short, rigid phenylene spacer between the porphyrin and the CCG. The composite material formed stable dispersions in DMF and the structure was characterized by spectroscopic, thermal, and microscopic measurements. In steady-state photoluminescence spectra, the emission from the porphyrin linked to the CCG was quenched strongly relative to that of the porphyrin reference. Fluorescence lifetime and femtosecond transient absorption measurements of the porphyrin-linked CCG revealed a short-lived porphyrin singlet excited state (38 ps) without yielding the porphyrin radical cation, thereby substantiating the occurrence of energy transfer from the porphyrin excited state to the CCG and subsequent rapid decay of the CCG excited state to the ground state. Consistently, the photocurrent action spectrum of a photoelectrochemical device with a SnO(2) electrode coated with the porphyrin-linked CCG exhibited no photocurrent response from the porphyrin absorption. The results obtained here provide deep insight into the interaction between graphenes and π-conjugated systems in the excited and ground states.     

Rectification in substituted atomic wires: a theoretical insight

Recently, there have been discussions that the giant diode property found experimentally in diblock molecular junctions could be enhanced by the many-body electron correlation effect beyond the mean field theory. In addition, the effect of electron-phonon scattering on an electric current through the diode molecule, measured by inelastic tunneling spectroscopy (IETS), was found to be symmetric with respect to the voltage sign change even though the current is asymmetric. The reason for this behavior is a matter of speculation. In order to clarify whether or not this feature is limited to organic molecules in the off-resonant tunneling region, we discuss the current asymmetry effect on IETS in the resonant region. We introduced heterogeneous atoms into an atomic wire and found that IETS becomes asymmetric in this substituted atomic wire case. Our conclusion gives the other example of intrinsic differences between organic molecules and metallic wires. While the contribution of electron-phonon scattering to IETS is not affected by the current asymmetry in the former case, it is affected in the latter case. The importance of the contribution of the electron-hole excitation to phonon damping in bringing about the current asymmetry effect in IETS in the latter case is discussed.     

Enantioselective direct aminalization with primary carboxamides catalyzed by chiral ammonium 1,1'-binaphthyl-2,2'-disulfonates

A highly effective catalytic enantioselective direct aminal synthesis was developed. Chiral ammonium 1,1'-binaphthyl-2,2'-disulfonates, which were prepared in situ from (R)-BINSA and achiral amines, promoted the enantioselective addition of primary amides to aromatic aldimines.     

Synthesis of 1,2-bisalkylidenecyclopentanes from 1,6-allenynes via stereoselective addition of nucleophiles to ruthenacyclopentenes

Ruthenium-catalyzed cyclization of 1,6-allenynes occurs via the addition of heteroatom nucleophiles to ruthenacyclopentenes, providing functionalized 1,2-bisalkylidenecyclopentanes in a highly regio- and stereoselective manner.