There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...

background: the efficacy of piper aduncum essential oil was evaluated against periplaneta americana adults and nymphs in the laboratory. methods : the plant essential oil at varying concentrations ranging between 10,000 to 80,000 ppm were placed inside glass beakers, rolled horizontally to ensure the essential oil covers all sides of the beakers and exposed to adults and nymphs of p. americana ...

see for instance [29]. Notice that the exponent p or q could be larger than N+2 N−2 . Hence the usual Sobolev space H 0 (Ω)×H1 0 (Ω) is not suitable to handle the problem. To study the problem (1.2) under the condition (1.3), a key observation was done by Hulshof and Van de Vorst [16], De Figueiredo and Felmer [9]. In order to solve this problem, the main idea is to destroy the symmetry between...

fumigant toxicity of various doses of essential oils (185.2, 370.4, 555.5, 740.7, 925.4, 1111.1, and 1296.3 µl/l water) from five officinal plants, including rosemary (rosmarinus officinalis), lavender (lavandula vera), fennel (foeniculum vulgare), tarragon (artemisia dracunculus)and summer savory (satureja hortensis)on two stored products pests, cowpea weevil (callosobruchus maculatus) and red...

background: progesterone has been suggested to contribute to the regulation of spermatogenesis and to facilitate the production of viable sperm. investigations have showed that polymorphism of progesterone receptor (pgr) is associated with some diseases. objective: to analyze the potential relationship between male infertility and the +331g/a and progins polymorphisms of pgr gene. materials and...

We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving Hardy–Cesàro and Hardy–Bellman operators. extend these results to product Hardy p⩽1. Moreover, boundedness of Hardy-Cesàro Hardy-Bellman operators various (Lebesgue, Hardy, BMO) is discussed. One our main tools an appropriate version Hardy–Littlewood–Paley inequality ‖fˆ‖Lp′,q≲‖f‖Lp,q.

abstract the grasses cold tolerance is the most important limiting factor for its cultivation in temperate regions, so using cold tolerant cultivars is essential for grasses successful cultivation. in order to evaluation freezing stress tolerance of several species of grasses, this study was conducted in agricultural faculty of ferdowsi university of mashhad as a factorial complete randomized b...