Sentence examples for modular norm of from inspiring English sources

The modular norm of Orlicz-Sobolev spaces is the natural generalization of the Luxemburg norm.

Analyzing and combining the properties of both Orlicz spaces and Sobolev spaces, we get the sufficient and necessary criteria for Orlicz-Sobolev spaces equipped with a modular norm to be uniformly rotund in every direction.

Then we can study the Orlicz-Sobolev spaces with modular norm by using the methods of Orlicz spaces.

In this section, we first of all discuss the relationships between modular and the modular norm which are similar to that of Orlicz spaces.

In the third section we give some relationships between a modular and the modular norm.

So we equip the Orlicz-Sobolev spaces with a modular norm and study Orlicz-Sobolev spaces.

In this paper, the modular-type operator norm of the general geometric mean operator over spherical cones is investigated.

This extension gives the Opic-Gurka-type estimate of the modular-type operator norm of the general geometric mean operator corresponding to (g(t)).

This extension gives the Persson-Stepanov-type estimate of the modular-type operator norm of the general geometric mean operator corresponding to (g(t)).

This extension gives Persson-Stepanov-type and Opic-Gurka-tpye estimates of the modular-type operator norm of the general geometric mean operator corresponding to (g(t)).

The main purpose of this paper is to investigate the property and the uniform Opial property equipped with the Luxemburg norm of the new modular sequence space, which is defined by using the generalized de la Vallée-Poussin mean with generalized Riesz transformation.