Norm related inequalities for fractional integrals

Fractional spline wavelet systems are considered in the work. Molecular structure of elements of such systems admits estimates connecting norms of fractional integrals' images and pre--images in Besov spaces.

[1]  Vladimir I. Clue Harmonic analysis , 2004, 2004 IEEE Electro/Information Technology Conference.

[2]  E. Ushakova Spline wavelet bases in function spaces with Muckenhoupt weights , 2020, Revista Matemática Complutense.

[3]  S. B. Stechkin,et al.  Basic wavelet theory , 1998 .

[4]  D. Haroske,et al.  Atomic decompositions of function spaces with Muckenhoupt weights ; an example from fractal geometry , 2005 .

[5]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[6]  K. Ushakova,et al.  Localisation property of Battle–Lemarié wavelets' sums , 2017, 1708.09536.

[7]  G. Battle A block spin construction of ondelettes. Part I: Lemarié functions , 1987 .

[8]  D. Haroske,et al.  Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I , 2008 .

[9]  E. Ushakova,et al.  Wavelet Bases and Entropy Numbers of Hardy Operator , 2018 .

[10]  B. Muckenhoupt Hardy's inequality with weights , 1972 .

[11]  V. Rychkov Littlewood-Paley Theory and Function Spaces withAlocp Weights , 2001 .

[12]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[13]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[14]  H. Triebel Theory Of Function Spaces , 1983 .

[15]  E. Ushakova,et al.  Hardy–Steklov Integral Operators: Part I , 2018 .

[16]  Svetlana Roudenko,et al.  Matrix-weighted Besov spaces , 2002 .

[17]  D. Haroske,et al.  Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis , 2008 .

[18]  Thierry Blu,et al.  Construction of fractional spline wavelet bases , 1999, Optics & Photonics.

[19]  B. Muckenhoupt,et al.  Weighted norm inequalities for the Hardy maximal function , 1972 .

[20]  Thierry Blu,et al.  Fractional Splines and Wavelets , 2000, SIAM Rev..

[21]  H. Triebel Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration , 2010 .

[22]  G. Battle A block spin construction of ondelettes Part II: The QFT connection , 1988 .

[23]  R. Askey Orthogonal Polynomials and Special Functions , 1975 .