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The goal of this paper is to develop the Littlewood--Paley theory of discrete Morrey spaces. As an application, we establish the boundedness of martingale transforms. We carefully justify the definition of martingale transforms, since discrete Morrey spaces do not contain discrete Lebesgue spaces as dense subspaces. We also obtain the boundedness of Riesz potentials. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy– Littlewood maximal operator for general Radon measure on ℝn. Earlier, the strong type vector-valued inequality for the same operator and the weak type vector-valued inequality for the dyadic maximal operator were obtained. This paper will supplement these existing results by proving a weak type counterpart.

The present paper supplements our earlier works. Our goal in the present paper is to establish the boundedness of generalized fractional integral operators from the Morrey space L1,φ(X;μ) to the Campanato space L1,ψ(X;μ) over non-doubling measure spaces (X, d, μ). What is new in the present paper is that μ satisfies a minimal condition; 0 = μ({x}) < μ(B(x,r)) < ∞ for all x ε X and r > 0. We first, review some elementary facts on the fractional integral operators, generalized Morrey spaces, and analysis on metric measure spaces. [ABSTRACT FROM AUTHOR]

Abstract The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding fails for . Brézis-Gallouët-Wainger and some other authors quantified why this embedding fails by means of the Hölder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.

We show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces.

We show the boundedness of fractional integral operators by means of extrapolation. We also show that our result is sharp.

We experienced a rare case in which iliopsoas abscess (IPA), caused by an Extended Spectrum β-Lactamase (ESBL)-producing Proteus mirabilis, perforated and communicated with the ureter and caused sepsis. An 84-year-old woman, bedridden due to sequelae of a cerebral hemorrhage, was brought to our hospital with a chief complaint of fever lasting for 3 weeks. Computed tomography (CT) revealed a huge 180 × 110 × 100 mm IPA in the right iliopsoas muscle. The ureter was also found to communicate with the iliopsoas muscle abscess, ureteral stenosis was detected at the same site, and dilatation of the renal pelvis occurred above the area of the ureteral stenosis, indicating hydronephrosis. Considering the mechanism of this case, if the ureter first ruptures and urine leaks, followed by the formation of an IPA, urine will flow along the surrounding fatty tissue and cause an abscess around the ureter and kidney. However, because almost no abscess was detected around the ureter, the abscess was thought to have originated from the iliopsoas muscle located near the center of the ureter. In summary, in this case, an abscess first formed within the iliopsoas muscle, which gradually expanded and compressed the right ureter, resulting in hydronephrosis. The upper ureter, which had become dilated and thinned due to ureteral obstruction, became even more fragile because of the spread of inflammation from the IPA, and the IPA perforated and communicated with the ureter. In patients who have difficulty communicating, the diagnosis of IPA may be delayed because the only symptom is fever. As in this case, if the diagnosis is delayed, the abscess may become large and perforate the ureter; thus, IPA should always be considered as a cause of fever of unknown origin., Competing Interests: None, (Copyright © Japan Medical Association.)

Introduction: Hemodialysis patients have various complications, and orthopedic diseases include carpal tunnel syndrome, spinal canal stenosis, spondylosis destruction, fractures, and osteoarthritis. As a treatment for knee osteoarthritis, intra-articular injections of hyaluronic acid and steroids are performed. In general, steroid injections have a strong short-term anti-inflammatory effect, but there is a risk of complications, such as infection. In addition to aging, dialysis patients are prone to weakened immune systems and susceptibility to infection. Therefore, more attention should be paid to the treatment of osteoarthritis in dialysis patients. This study aimed to compare the effects of steroid and complication of infection of dialysis and non-dialysis patients who underwent intra-articular steroid injection., Methods: A total of 20 dialysis patients (23 knees) and 20 non-dialysis patients (24 knees) with knee osteoarthritis who underwent steroid injections were investigated. All patients underwent radiographic diagnosis and were evaluated for the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) score, visual analog scale (VAS), range of motion (ROM), and side effects before, and at 3, and 6 months after injection., Results: The mean body mass index (BMI) was 21.3 (±standard deviation (SD) 2.8) and 24.9 (±SD 2.6) in dialysis and non-dialysis patients, respectively, showing a significant difference. Both dialysis and non-dialysis patients showed statistically significant improvement in VAS and WOMAC scores after steroid injection. There were no significant differences between dialysis and non-dialysis patients in the gender differences and mean age. There were no infection complications in both groups., Conclusions: This study revealed the analgesic effect of steroids on knee osteoarthritis in dialysis and non-dialysis patients. On the other hand, there were no infection complications in either patient. These findings suggest that intra-articular steroid injection is safe for dialysis patients., Competing Interests: None, (Copyright © Japan Medical Association.)

Background: Age-related declines in cognitive function and cerebral perfusion increase the risk of dementia. Although nutrition and exercise may be effective in reducing cognitive decline, the effect of lactotripeptide (LTP) on cerebral oxygenation and hemodynamics remains unclear., Objectives: The aim of this study was to investigate the effects of LTP ingestion on cerebral oxygenation, cognitive function, and vascular function in middle-aged and older adults with or without an exercise intervention., Methods: We recruited 2 separate groups of participants, one with and one without an exercise intervention. Each group was then randomly assigned into a placebo group and an LTP group. The participants ingested a placebo or LTP every day. The exercise group performed aerobic exercises 4-6 d/wk. Before and after the 8-wk intervention, we measured oxygenated hemoglobin (oxy-Hb) concentration (oxy-Hb change) in the prefrontal cortex during the Stroop task (primary outcome), Stroop interference time, and carotid artery β-stiffness (both secondary outcomes)., Results: Sixty-four participants completed the study. Changes in oxy-Hb signal in the prefrontal cortex were greater in the LTP group than in the placebo group under both the exercise and nonexercise conditions (P < 0.05). In addition, the magnitude of improvement in the oxy-Hb change in the left prefrontal cortex was correlated with Stroop interference (r = -0.39, P < 0.05) and carotid β-stiffness (r = -0.41, P < 0.05)., Conclusions: An 8-wk intake of LTP increased cerebral oxygenation in the prefrontal cortex region in middle-aged and older adults, with and without exercise. The intervention-induced improvements in brain neural activation were associated with cognitive and vascular function. This trial was registered at www.umin.ac.jp as UMIN000022313.

Age-related decreases in cognitive function, cerebral perfusion, and vascular function increase the risk of dementia. However, the effects of central artery stiffness on cerebral oxygenation hemodynamics during executive function tasks and executive function remain unclear. The aim of this cross-sectional study was to investigate the relationships among central artery stiffness, cerebral oxygenation hemodynamics during executive function tasks, and executive function in middle-aged and older adults. Sixty-two middle-aged and older adults (age range: 51-79 years) were recruited for this study. For each participant, we measured the carotid artery β-stiffness, oxygenated hemoglobin (oxy-Hb) signal change in the prefrontal cortex during the Stroop task, and Stroop interference time. Correlation analyses revealed that the carotid artery β-stiffness was significantly correlated with the Stroop interference time (r = 0.43, P < 0.001) and with the oxy-Hb signal change in the left (r = -0.38, P = 0.002), but not the right, prefrontal cortex. In addition, the Stroop interference time was significantly correlated with the oxy-Hb signal change in the left (r = -0.42, P = 0.001), but not the right, prefrontal cortex. The participants were divided into the low and high arterial stiffness groups according to the median value. We found that the Stroop interference time was significantly shorter (P = 0.006) and the oxy-Hb signal change in the left prefrontal cortex was significantly larger in the low arterial stiffness group than in the high arterial stiffness group (P = 0.011). In the low, but not the high, arterial stiffness group, the oxy-Hb signal change of the left prefrontal cortex during executive function tasks was significantly larger than the oxy-Hb signal change of the right prefrontal cortex (P = 0.014). These results suggest that increases in central artery stiffness are associated with decreases in oxygenation hemodynamics in the left prefrontal cortex during executive function tasks and reductions in executive function., (Copyright © 2018 Elsevier Inc. All rights reserved.)