TY - CHAP

T1 - More on hypersingular integrals and embeddings into hölder spaces

AU - Kokilashvili, Vakhtang

AU - Meskhi, Alexander

AU - Rafeiro, Humberto

AU - Samko, Stefan

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this chapter we present results on hypersingular operators of order α < 1 acting on some Sobolev type variable exponent spaces, where the underlying space is a quasimetric measure space. The proofs are based on some pointwise estimations of differences of Sobolev functions. These estimates lead also to embeddings of variable exponent Hajlasz-Sobolev spaces into variable order Hölder spaces. In the Euclidean case we prove denseness of C∞0-functions in W1,p(·)(Rn). Note that in this chapter we consider quasimetric measure spaces with symmetric distance: d(x, y) = d(y, x).

AB - In this chapter we present results on hypersingular operators of order α < 1 acting on some Sobolev type variable exponent spaces, where the underlying space is a quasimetric measure space. The proofs are based on some pointwise estimations of differences of Sobolev functions. These estimates lead also to embeddings of variable exponent Hajlasz-Sobolev spaces into variable order Hölder spaces. In the Euclidean case we prove denseness of C∞0-functions in W1,p(·)(Rn). Note that in this chapter we consider quasimetric measure spaces with symmetric distance: d(x, y) = d(y, x).

UR - http://www.scopus.com/inward/record.url?scp=85007188995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007188995&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-21015-5_8

DO - 10.1007/978-3-319-21015-5_8

M3 - Chapter

AN - SCOPUS:85007188995

T3 - Operator Theory: Advances and Applications

SP - 439

EP - 454

BT - Operator Theory

PB - Springer International Publishing

ER -