We investigate Bergman type operators on the complex unit ball, which are singular integral induced by modified kernel. consider $L^p$-$L^q$ boundedness and compactness of operators. The results can be viewed as Hardy–Littlewood–Sobolev (HLS) theorem in case ball. also give some sharp norm estimates fact gives upper bounds optimal constants HLS inequality Moreover, a trace formula is given.

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...

Let f be a number-theoretic function. A finite set X of natural numbers is called f -large if card(X) ≥ f(min(X)). Let PHf be the Paris Harrington statement where we replace the largeness condition by a corresponding f -largeness condition. We classify those functions f for which the statement PHf is independent of first order (Peano) arithmetic PA. If f is a fixed iteration of the binary lengt...

It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure ...

Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)....

‘Hardy 2519’ (Reg. no. CV-1189, PI 692613), a hard red winter (HRW) wheat (Triticum aestivum L.) cultivar, was derived from the cross VA06HRW-108 × ‘Vision 30’ (PI 661153) using modified bulk breeding method. Hardy 2519 tested as VA14HRW-25 in replicated yield trials Virginia (2015–2018) and USDA-ARS Uniform Bread Wheat Trials (2016–2018) released by Agricultural Experiment Station 2019. is wid...

Hardy persons are hypothesized to be resistant to stress-induced illness, because of their adaptive cognitive style and a subsequently reduced level of physiological arousal. We assessed the cognitive and physiological responses of high and low hardy male undergraduates to a challenging task under high and low evaluative threat. As predicted, hardy subjects endorsed more positive self-statement...

We define a Muckenhoup-type condition on weighted Morrey spaces using the Köthe dual of space. show that is necessary and sufficient for boundedness maximal operator defined with balls centered at origin spaces. A modified characterizes inequalities Calderón operator. also local usual Hardy–Littlewood operator, simplifying previous characterization Nakamura–Sawano–Tanaka. For same in case globa...