A trace inequality of Riesz potentials in variable exponent Orlicz spaces

2012 ◽  
Vol 285 (11-12) ◽  
pp. 1466-1485
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Variable Exponent ◽  
Orlicz Spaces ◽  
Trace Inequality ◽  
Riesz Potentials

scholarly journals A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

2012 ◽  
Vol 98 (3) ◽  
pp. 253-263 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Orlicz Spaces ◽  
Riesz Potentials ◽  
Nirenberg Inequality

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

Weighted Morrey spaces of variable exponent and Riesz potentials

2014 ◽  
Vol 288 (8-9) ◽  
pp. 984-1002 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Riesz Potentials ◽  
Weighted Morrey Spaces
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