The critical weighted inequalities of the spherical maximal function

Weighted inequality on the Hardy-Littlewood maximal function is completely understood while it is not well understood for the spherical maximal function. For the power weight $|x|^{\alpha}$, it is known that the spherical maximal operator on $\mathbb{R}^d$ is bounded on $L^p(|x|^{\alpha})$ only if $1-d\leq \alpha<(d-1)(p-1)-d$ and under this condition, it is known to be bounded except $\alpha=1-d$. In this paper, we prove the case of the critical order, $\alpha=1-d$.Comment: 14 page

Competitiveness of textile and apparel industries in the United States and Japan

The purpose of this study was to examine how the textile and apparel industry competitiveness in developed countries, namely the United States and Japan, related to trade and productivity between 1962 and 2010. The United States and Japan were selected for this study because of their similar economic development levels, each having its unique strategy to increase domestic textile and apparel industry competitiveness. This study proposed a theoretical framework based on competitive advantage theory, comparative advantage theory, and new growth theory to determine the relationship between trade balance and the principle goal of industrial competitiveness and between productivity and the principle goal of industrial competitiveness. This research used neoclassical theory to measure productivity. This study used two stages to test the research hypotheses: (a) preliminary and (b) the Granger causality test. Preliminary data analysis included (a) a data cleaning procedure; and (b) the Granger causality test\u27s assumption check by conducting analysis of a stationarity test; and (c) descriptive statistics. The Granger causality test included: (a) identification of time lag structure for the Granger causality regression models using F-statistics and t-statistics; and (b) interpretation of the final Granger causality models with statistically significant lag structures found (Granger, 1969). The research found that there was no relationship between trade balance and the principle goal of industrial competitiveness in the U.S. and the Japanese textile and apparel industries. This research found that income growth had a negative causal effect on trade balance growth in the Japanese apparel industry, even though there was no causal effect of trade balance growth on income growth found. For both the U.S. textile industry and the Japanese textile and apparel industries, no causal relationship was found between productivity and the principle goal of competitiveness. However, the study did find that there was a causal effect of productivity on the principle goal of industrial competitiveness in the U.S. apparel industry. This research has both theoretical and practical implications for textile and apparel industries in developed countries. Theoretically, this study provided a comprehensive definition of competitiveness that clarifies the major construct of Michael Porter\u27s Competitive Advantage Theory. Practically, the research provided different strategies for apparel and textile firms or industries with different focus in developed countries. Textile and apparel firms with strong domestic production will need to restructure their strategies to focus on high value added activities and to decrease the production function to be able to increase their industrial competitiveness with trade balance and productivity growth. Textile and apparel firms with strong high value added functions such as innovation and product strategy as well as marketing and supply chain management which created a global brand should focus on increasing trade balance and productivity because they are both positively related to their industrial competitiveness

U.S. Cotton Industry Competitiveness in the Context of the Cotton Supply Chain

The U.S. cotton industry generates more than $25 billion in products and related services yearly, employing approximately 200,000 people in the various industry sectors from farms to textile mills (USDA, 2013a). Of the total cotton production in the United States, 75% is currently exported, leading to the importance of competitiveness of the U.S. cotton industry in a global setting. The United States has been the top cotton exporter in the world since 1989, accounting for nearly one-third of the world\u27s cotton exports (USDA, 2013b). However, the market leadership has been consistently challenged, resulting in a significant decrease in the market share of the U.S. cotton export from 41.24% in 2004 to 26.70% in 2013 in the global cotton market (USDA, 2013b). Traditionally, the textile and apparel industries are considered an extended part of the cotton supply chain because textile and apparel industries have used and are using raw materials from the cotton industry to create final products for consumers at the final stage of the cotton supply chain (Rivoli, 2009). However, there has been little research to investigate how U.S. cotton industry competitiveness is affected in the context of the cotton supply chain. Based on this, there exists a need to understand the current competitiveness of the U.S. cotton industry, as well as how to improve this position on a global scale in the context of cotton supply chain. Therefore, the purpose of this research is to preliminarily explore factors that determine the competitiveness of the cotton industry in the context of cotton supply chain based on Porter\u27s competitiveness factor model