The aim of this paper is to define the Besov-Morrey spaces and the TriebelLizorkin-Morrey spaces and to present a decomposition of functions belonging to these spaces. Our results contain an answer to the conjecture proposed by Mazzucato.

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The MRL-lpr/lpr(MRL/l) mouse is a new animal model for human systemic lupus erythematosus (SLE) and skin lesions with hair loss and scab formation are one of the characteristic manifestations in this mouse. We investigated the histopathology of the skin lesions in MRL/l mice and studied the related autoimmune phenomenon. Light microscopical observations revealed hyperkeratosis, acanthosis, hypergranulosis, liquefaction, vasodilation in the dermis and T-cell infiltration into the dermis at the age of 5 months (mo). Immunohistological studies showed the presence of immunoglobulins and/or complement depositions at the dermal-epidermal junction (DEJ). In some mice there was deposition of immunoglobulin at the DEJ at 2 mo and in 90%-100% of MRL/l mice at over 5 mo. Temporal relationship was present among cutaneous immunoglobulin depositions, the occurrence of anti-DNA antibodies and proteinuria. These findings suggest that MRL/l mice might provide a new aid for studying the biological mechanisms of the development of skin lesions in human SLE.

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Spontaneous current jump resulting in the formation of closed field equilibrium has been observed in electron-cyclotron-heated toroidal plasmas under steady external fields composed of a toroidal field and a relatively weak vertical field in the low aspect ratio torus experiment device. This bridges the gap between the open field equilibrium maintained by a pressure-driven current in the external field and the closed field equilibrium at a larger current. Experimental results and theoretical analyses suggest a current jump model that is based on the asymmetric electron confinement along the field line appearing upon simultaneous transitions of field topology and equilibrium.

Main objective of the LATE (Low Aspect ratio Torus Experiment) device is to demonstrate formation of ST plasmas by electron cyclotron heating (ECH) alone without center solenoid. By injecting a 2.45 GHz microwave pulse up to 30 kW for 4 seconds, a plasma current of 1.2 kA is spontaneously initiated under a weak steady vertical field of B v = 12 Gauss, and then ramped up with slow ramp-up of B v for the equilibrium of the plasma loop and finally reaches 6.3 kA at B v = 70 Gauss. This currents amount 10 percents of the coil currents of 60 kAT for the toroidal field. Magnetic measurements show that an ST equilibrium, having the last closed flux surface with an aspect ratio of R 0 /a 20.4 cm/14.5 cm 1.4, an elongation of κ = 1.5 and q edge = 37, has been produced and maintained for 0.5 s at the final stage of discharge. The plasma center locates near the second harmonic EC resonance layer and the line averaged electron density significantly exceeds the plasma cutoff density, suggesting that the second harmonic EC heating by the mode-converted electron Bernstein waves (EBW) support the plasma. Spontaneous formation of ST equilibria under steady B v fields, where plasma current increases rapidly in the time scale of a few milliseconds, is also effective and a plasma current of 6.8 kA is spontaneously generated and maintained at B v = 85 Gauss by a 5 GHz microwave pulse (130 kW, 60 ms).

Abstract. The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under pointwise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The boundedness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the FeffermanPhong inequality is given by the use of the characteristic function of the Cantor set.

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