| Preface | p. ix |
| Acknowledgments | p. xiii |
| Basic notation | p. xv |
| Hardy-Type Operators | p. 1 |
| Boundedness and compactness in BFS | p. 1 |
| An extension of the Hardy transform | p. 25 |
| Estimates for approximation numbers | p. 44 |
| Norms of positive operators | p. 57 |
| Notes and comments on Chapter 1 | p. 75 |
| Fractional Integrals on the Line | p. 77 |
| Fractional integrals | p. 77 |
| Two-weight problems | p. 102 |
| Trace inequalities ("Diagonal case"). Examples | p. 107 |
| Weak-type inequalities. Examples | p. 135 |
| Integral transforms with power- logarithmic kernels | p. 141 |
| Erdelyi-Kober operators | p. 154 |
| Integral transforms with positive kernels | p. 160 |
| Extended Erdelyi-Kober operators | p. 185 |
| Generalized one-sided potentials | p. 198 |
| One-sided potentials on the half-space | p. 218 |
| Weighted criteria in Lorentz spaces | p. 230 |
| Applications to Abel's integral equations | p. 241 |
| On some Volterra-type integral equations | p. 244 |
| Application to the existence of positive solutions of nonlinear integral equations | p. 246 |
| Notes and comments on Chapter 2 | p. 248 |
| One-Sided Maximal Functions | p. 251 |
| One-sided maximal functions | p. 251 |
| Mapping properties of potentials on the line | p. 256 |
| Potentials T[subscript gamma] on the line (the case 0 [less than sign] [gamma] [less than sign] 1/p) | p. 267 |
| Weak-type inequalities | p. 275 |
| Potentials on bounded intervals | p. 279 |
| Two-weight criteria for fractional maximal functions | p. 281 |
| Generalized one-sided maximal functions | p. 283 |
| Potentials with power-logarithmic kernels | p. 288 |
| Multiple potentials | p. 296 |
| One-sided Hormander-type maximal functions | p. 310 |
| Notes and comments on Chapter 3 | p. 315 |
| Ball Fractional Integrals | p. 317 |
| Boundedness criteria | p. 317 |
| Compactness criteria | p. 328 |
| The measure of non-compactness | p. 334 |
| Mapping properties in Lorentz spaces | p. 338 |
| Notes and comments on Chapter 4 | p. 341 |
| Potentials on R[superscript N] | p. 343 |
| Truncated potentials | p. 343 |
| Two-weight compactness conditions for Riesz potentials | p. 359 |
| Integral transforms with radial kernels | p. 362 |
| Notes and comments on Chapter 5 | p. 365 |
| Fractional Integrals on Measure Spaces | p. 367 |
| Integral transforms on nonhomogeneous spaces | p. 367 |
| Theorems of Adams type | p. 376 |
| Truncated potentials on SHT | p. 380 |
| Riesz potentials in the half-space | p. 389 |
| Truncated potentials in the half-space | p. 397 |
| Two-weight (p, p) type inequalities | p. 412 |
| Theorems of Koosis type | p. 428 |
| Fractional maximal functions on SHT | p. 437 |
| Weighted estimates in Lorentz spaces | p. 441 |
| Notes and comments on Chapter 6 | p. 446 |
| Singular Numbers | p. 447 |
| Volterra integral operators | p. 447 |
| Riemann-Liouville-type operators | p. 461 |
| Potential-type operators | p. 476 |
| Hardy-type operators | p. 482 |
| Asymptotic behaviour of singular and entropy numbers | p. 488 |
| Notes and comments on Chapter 7 | p. 498 |
| Singular Integrals | p. 501 |
| Two-weight strong-type estimates | p. 502 |
| Weak-type estimates | p. 522 |
| Singular integrals on nonhomogeneous spaces | p. 541 |
| Two-weight inequalities for the Hilbert transform | p. 552 |
| Estimates in Lorentz spaces | p. 557 |
| Cauchy-Szego projection | p. 578 |
| Singular integrals via Clifford analysis | p. 584 |
| Theorems of Koosis type | p. 587 |
| Notes and comments on Chapter 8 | p. 592 |
| Multipliers of Fourier Transforms | p. 593 |
| Weighted Triebel-Lizorkin spaces | p. 593 |
| Two-weight multipliers in Triebel-Lizorkin spaces | p. 598 |
| (F[superscript q, theta] [subscript beta, omega] F[superscript p,theta] [subscript beta, upsilon]) multipliers. The case 1 [less than sign] q [less than or equal] p [less than sign] [infinity] | p. 609 |
| Multipliers in weighted spaces with mixed norms | p. 610 |
| Examples | p. 613 |
| Notes and comments on Chapter 9 | p. 615 |
| Problems | p. 617 |
| References | p. 622 |
| Index | p. 640 |
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