19 research outputs found
Weighted <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-approximation with positive linear operators on unbounded sets
The estimates of approximation by using a new type of weighted modulus of continuity
WOS: 000248144000012In this paper, we introduce a new type modulus of continuity for function f belonging to a particular weighted subspace of C (0, infinity) and show that it has some properties of ordinary modulus of continuity. We obtain some estimates of approximation of functions with respect to a suitable weighted norm via the new type moduli of continuity. Finally, we give some examples. (C) 2007 Elsevier Ltd. All rights reserved
The Stein-Weiss type inequalities for the B-Riesz potentials
We establish two inequalities of Stein-Weiss type for the Riesz potential operator I?,? (B-Riesz potential operator) generated by the Laplace-Bessel differential operator ?B in the weighted Lebesgue spaces Lp,|x|ß,?. We obtain necessary and sufficient conditions on the parameters for the boundedness of I?,? from the spaces Lp,|x|ß,? to Lq,|x|-?,?, and from the spaces L1,|x|ß,? to the weak spaces WLq,|x|-?,?. In the limiting case p=Q/? we prove that the modified B-Riesz potential operator I?,? is bounded from the spaces Lp,|x|ß,? to the weighted B-BMO spaces BMO|x|-?,?. As applications, we get the boundedness of I?,? from the weighted B-Besov spaces Bs p?,|x|ß,? to the spaces Bs q?,|x|-?,?. Furthermore, we prove two Sobolev embedding theorems on weighted Lebesgue Lp,|x|ß,? and weighted B-Besov spaces Bs p?,|x|ß,? by using the fundamental solution of the B-elliptic equation ??/2 B